text:
Recommendation Letter from a non Phd faculty member - URGENT!
I am applying for MS/PhD in Petroleum Engineering. My dilemma is that my academic project is under a non-PhD faculty member. She is currently undergoing PhD. Would it be wise to take LOR from her? I am thinking of applying to MS because my LOR's wont be strong enough for PhD in my opinion. Suggestions please

I am thinking of applying to MS because my LOR's wont be strong enough for MS in my opinion. Do you mean you are not applying for PhD instead of MS?

If it was so extremely urgent, you would have read the information that already exists, instead of waiting for people to write brand-new answers: http://academia.stackexchange.com/q/49865/8705 http://academia.stackexchange.com/q/49322/8705 http://academia.stackexchange.com/q/58323/8705

If you've been working on research with her, then it should be fine. It's akin to asking a boss in industry to write a LoR for you if you were applying for an MS/PhD after several years in industry.
Additionally, most programs ask for at least 2 LoRs, so just make sure the second one is from a PhD-holding faculty member.

Thanx  a lot,
Would it work even if I am applying for a PhD program?

I see no reason why it wouldn't :-)

I got into a PhD program with three industry LoR's. At most one of the writers had a PhD.

When it comes to graduate school applications the fact that your reccomendation is from a faculty member is orders of magnitude more important than their credentials. (unless they are a undisputed leader in a field, then credentials might matter, but not negatively.)


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What do I need to do as a potential mature student in the UK?
Please bear with me in this question despite its length. I'm only putting so much detail in it because I want to be thorough, as this is an important subject to me.
I'll explain my situation first as to provide some context for my dilemma - I'm 19 years old, soon to be 20 in a few months, and I decided last year that I wasn't ready for university for a number of reasons. The most prominent of these were a fear of falling into debt, not being able to support myself while there and also not being sure of what career path I wanted to pursue. In light of that, I decided to apply for an apprenticeship at a fairly prestigious but small software design company in the field of Business Intelligence. I got the job (and am on the way to completing the level 4 diploma in "Information Technology, Programming and Networking) and will be employed until 21, when my contract ends. Over that period of time I'll be able to save up a fairly substantial amount of money (for me),
I'm convinced now that I want to apply to a few of the top universities in the UK for Computer Science once my contract is over, but my A-level results aren't quite up to scratch for these. For reference, I have an A, B and a C in Computer Science/Psychology/Music Technology, respectively. What I needed was three A's. The universities I have in mind are Birmingham, Bath, the Imperial College of London, and Oxford and Cambridge - just on the off-chance I somehow get in or attain the necessary qualifications. The exact course that I've looked at is a five-year long MSci in Computer Science with a year of industry work/study abroad.
As a mature student though, I understand that I'll be subject to different entry requirements. One of these is an access to higher education course, but there aren't any within 50 miles of me that I can do a relevant course in via distance learning or even just evening classes, which means I'd need to do such a course after I finish my work contract in November 2016, further extending the amount of time before I can begin a degree.
If anyone has any experience in applying to a highly ranked university - especially in the field of computer science - as a mature student, is there any advise that you can give me?
As an extra note, I have emailed the universities in question to ask them for their advice and what would be expected of me when it comes to applying as a mature student. I haven't heard back yet, but I only sent an email last week.

Hi Steven, I don't have much for you on the substance of your question but just rest assured, the universities were likely shut for Easter last week. Hence the non-replies on the email.

Thank you for your comment regardless, that's reassuring to know.

I went to the UK to start my undergraduate when I was 27.  I was also not able to access the normal 'go-to-class' higher education courses.  My path wasn't computer science, but I think the general rules and requirements are roughly the same for each course.
In a mature student, UK universities are typically looking for enthusiasm, evidence that they are interested in the subject they are applying for, and that they are capable of doing university work.  Ideally what they want to see is that you have done some systematic course of study, typically in the last three years.  You have this (A-Levels and the diploma).  They also value experience - which you are getting by being in work in the area you want to pursue a degree in.
Your A-Level results aren't bad at all, but as you note fall short of what they usually want.   With your work experience and additional formal certification, it is possible that the universities will look more favourably on your application.  Remember that even if you were to go into university straight from A-Level, grade requirements aren't hard and fast rules.  Which leads me to the next bit that is important - the personal statement.  This is the point at which you can say that you are more than capable of doing the course.  Don't dwell on your A-Level results, they can already see them.  Instead you sell yourself.  Really- this can make an application very attractive!  It's not all about grades - especially when you are a mature student.
If you did want to pursue another formal course, have you looked at the Open University options?  I did one of their courses (one 10 credit course) as I had been nearly 10 years out of education, and quite frankly my A-Level results were not...great.  It needed a lot of commitment to study and work full time, but overall it was a good experience, and I felt the course was delivered well.  If you can find something there that is relevant, I can highly recommend them.

When you suggest an open university course, do you mean as an alternative to the undergraduate course I'm currently taking or as a means to provide myself with an additional favourable qualification before applying to the mentioned universities? I don't think I'd have much trouble doing an OU course while I work until the end of my contract as my evenings are mostly free. However, if you mean as an alternative that raises a new question altogether. I'll save that until I get a reply from someone on that topic though.

Sorry, poor phrasing. I meant: "Do you mean as an alternative to the undergraduate course I'm currently thinking of taking or..."

I was thinking more of an addition to your A-Levels to enhance your chances of being accepted onto the MSci IF the universities say there is an issue with your grades being a bit lower than they would want... just another avenue to explore (every university is different, but to be honest, I would have thought your work experience/diploma would be enough to give you the extra boost)

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I want to transition from Mathematics to Computer Science for a PhD. Will post-baccalaureate studies in Computer Science help me?
In order to better understand my questions it is best to provide some context to them.
Background: I completed a B.Sc. degree in pure mathematics several years ago. I kept in contact with my letters of recommenders (their letters are strong), and published in an undergraduate mathematics journal. I want to transition from mathematics to computer science for a PhD program. I delayed my entrance into a PhD program to work in industry. Now I am in a position where I can enter back into school.
The problem I face is that 1) I lack many of the preliminary courses required by many PhD programs in Computer Science and 2) My GPA is on the low side due to extenuating circumstances during those respective semesters (which relates to my reasons of delaying a PhD to pursue industry work).
The PhD programs I am interested in are very competitive. I contacted a professor at one of these universities (nationally ranked & well-known) and he said he'd vouch for me whenever I applied and a few of my recommenders know him personally. But according to the school's website individual faculty have little input in admission decisions (as admissions is determined by a group of faculty) and they seem to have a strict set of coursework requirements needed in order to be admitted into their program. Also, my GPA falls outside the range of the "average" admitted students.
So, even though I have strong LoRs, strong research experience and a professor interested in me, I have a low GPA and not nearly enough of the core courses to satisfy their coursework requirements.
I applied/was accepted to do a post-bac at a well-regarded school. I will be a credit (but non-degree seeking) undergraduate student and can take any range of courses I want (both undergrad + grad).
Question:
1) Will pursuing a post-bac route help me get into a CS PhD program? My aim here is to complete the core set of requirements, bolster my GPA, and make myself competitive for PhD programs in CS (I don't want to do an MS program). Since I lack basic CS coursework I'll be taking courses in programming, data structures, analysis of algorithms, computer organizations and the like.
2) When will be the best time to apply for PhD programs? I plan to take courses on a part-time basis (since I am working full-time), so a max of 1-2 courses a semester. I was thinking if I applied next Fall then I'd only have two programming courses completed (required sequence), and a data structure course in progress. I still wouldn't have completed analysis of algorithms, etc. courses by that time. Luckily, I already taken all of the program's math requirements with high marks.
3) Is it fine to not satisfy every coursework requirement in the list? It is also recommended to have other courses completed outside of the core, but I am very eager to get the core completed and move into research. Lastly, would a B in any of these courses be a death kneel for my purpose? Some of these courses have a reputation of being extremely difficult.
Thanks for the help!

What is your GPA? (Or if you don't want to share that, can you give a range or an upper bound?)

What is the purpose of the PhD as opposed to a second Master's or Post-Master's?

@Compass I want to pursue a PhD because I want a career in academia. A PhD program will involve research & will be fully funded, whereas a Masters will be coursework focused (potentially thesis based) and not fully funded.

@Sid Hard to say as I attended more than one place. Between 2.9-low 3.0 range.

Meant to add, I have A's in areas of math I intend to specialize in/use in graduate school (for CS), but my overall GPA was deflated.

You say "Some of these courses have a reputation of being extremely difficult.". You should look into what makes them difficult. For many CS students, constructing a valid proof is extremely difficult. You are unlikely to have much trouble with any courses that are considered difficult primarily because they require mathematical proofs.

@PatriciaShanahan I didn't realize that, but very good point. You are correct. The Design & Analysis course is suppose to be difficult due to the mathematical proofs involved, which is something I feel more comfortable with.

What you can do is first complete a masters degree in CS and then transition to a PhD program. Some masters programs do not require a bachelor degree in CS, and you can get your degree in 1~2 years after completing all the necessary courses.
While doing your masters degree, you get to know the professors, learn about their projects and gauge your ability to launch a career in computer science. That's also a great opportunity for you to find out if there could be an advisor-student match that will materialize into a PhD thesis.
If you then manage to get into the PhD program in the same institution, you may be able to transfer the credits and take the preliminary exams right away. Speak to the Graduate Advisor to find out more.
Good luck!

@nonary specifically said they didn't want to do an ms though...

I teach in the post-bac CS program at Mills College, which is aimed at people (like you) who have earned a bachelor's degree in a field other than CS and want to transition into CS, either for industry or to prepare for a CS PhD.  Two such students were subsequently admitted to the CS PhD program at University of Washington, one of the top programs in the country.  Others have gone on to CS PhD programs at UCSD and The University of Virginia.  I can provide more details privately.
There are many ways to take the prerequisite courses -- online, as a special student, etc.  The advantages of taking them in a post-bacc program (or at least the program I am most familiar with) are:

The classes are small, and many of the students are in the same situation as you, rather than to a profile you do not fit.
Because the classes are small and taught by full-time professors, you can get strong detail-filled letters by professors who know you well.
Being a full-time student makes you eligible for summer internships. For example, one of our recent students interned at NASA, which I'm sure helped him get admitted to PhD programs.
Depending on the school and your field, there may be research opportunities there. Research experience is very valuable for graduate school admissions.
You can boost your GPA. Your undergraduate GPA will seem a lot less important if you've earned excellent grades more recently in a CS program.

The biggest downsides of a post-bac program are that they're expensive, they take time, and the piece of paper is not worth much in itself.  (We have both a post-bac certificate program and an MA in Interdisciplinary Computer Science, which requires more coursework and a thesis and is a valuable piece of paper.)
I think you should carefully examine the costs and benefits of a post-bac program versus a terminal MSCS, rather than dismissing the latter.  After either, you will be in a good position to apply for a CS PhD program.
(Anyone with questions about the Mills program should feel free to contact me through my email address, which is easy to find.)

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How does the admissions process work for Ph.D. programs in Country X?
This is a special community wiki 'canonical' question that aggregates advice on a frequently-asked question. See this meta discussion. Please feel free to edit this question to improve it.
Please give answers here that explain in a bit of detail what the doctoral level application process is like in a specific country. Make it clear at the beginning which country.
Mention, also, if there are many exceptions to the process you describe. Feel free to edit answers to provide additional information, and, especially field specific information. The focus of this question is on the admissions process, not the process of completing a degree after admission; however, if a country's PhD process has unusual aspects that applicants should be aware of, please do describe these briefly.
The intent of this canonical question is to clear up for students, usually cross-border students, what they can expect in making an application and how it will be evaluated. Answers can also be an aid to people answering questions. For example, there are differences between Canada and the United States in doctoral education and it is often useful to understand that when answering specific questions.

Answers have been provided for:

Australia

Brazil (To Be Done)

Canada (To Be Done)

China  (To Be Done)

England and the UK

France

Germany

India (To Be Done)

Ireland (To Be Done)

Italy

Japan

Netherlands

Norway (To Be Done)

Russia

Sweden

Switzerland (To Be Done)

United States

This sort of thread also seems like a good potential use case for version labels if it gets rolled out on sites other than SO.

When many people ask this question, I get the feeling that the real question they're asking is "should I contact professors directly?".  Each  country's answer should probably have a section that addresses this directly.

Germany germany
While such things like graduate colleges (with more... structured programs) exist, the typical way is different.
Prerequisites
PhD studies (or, actually, a doctorate) in Germany typically take between 3 and 5 years. They might take longer, 6 or even 10, but the typical minimal time in terms of required funding and general expectation is 3 years.
Typically, you need a Masters degree for a PhD. While few universities and departments offer loopholes for a Bachelor degrees (commonly known as a fast-track), it's risky, uncommon and sometimes discouraged.
The in-country BSc takes 3 years, an MSc takes 2 years, and a PhD 3 years (or more, per above). Typically, the PhD is oriented purely towards research and therefore, arguably, not a "program" in the common understanding. Formal courses or other requirements are typically non-existing (except for graduate colleges).
Supervision
A German PhD is a kind of personal affair between the supervisor (a professor, but some other options exist) and the candidate. If a candidate cannot have a working relationship with the supervisor, the chances for a successful PhD are dim.
If you want to start a PhD, you ask a professor, if a mentorship / supervision is possible - either formally, by applying for a funded position (see below), or informally. You might get invited for a personal talk where the supervisor-to-be tries to find out where your interests lie and if you would fit personality-wise.
Important for people from the US: there are no centralised graduate admissions. The supervision is a personal matter of a PhD supervisor.
Position
An agreement to supervise a PhD student does not necessarily mean funding. It's the agreement to guide the student in their research, to give them ideas, to give them an opportunity to bounce ideas, to write papers together.
There are paid positions for doctorate students available. Typically, people occupying them aim to get their PhD. This is actually the norm in STEM fields. But an agreement to supervise does not necessarily come with such a position.
Multiple opportunities for a position exits, see below.
University-funded position
Think: TA. You get a contract with the university, are obliged to do something related to your topic of work there, e.g., help with the lectures of "your own" professor.
Typically, departments have some slots for students, funded by the university itself, that are specifically allocated for a prospective PhD candidate.
Third-party funding (Drittmittelstelle)
Drittmittel are external grants (in contrast to the state-provided funds that are used to pay the university funded positions). With the Drittmittel-funds, positions are created at the university that a PhD student might occupy. Even though the funding is through external grant money, the student will be employed by the university. These positions are typically advertised by the university and are for a limited time only (for the duration of the grant project).
The grant is typically tied to a specific project, if the PhD candidate is lucky, the topic of the project can be turned into the PhD topic, otherwise the PhD candidate will have to do most of the PhD research on the side. Some grants will only be for 2 years, not enough to complete the PhD, so there is often the need to find a follow-up position to finish the PhD. Because of this, PhD students on Drittmittel-positions might need to be actively involved in project and grant acquisition.
Stipend from a foundation or the DAAD
Being an extraordinary (foreign) student, or doing a lot of volunteering, etc. might score you a stipend from a foundation (Stiftung), e.g. from an organisation close to a political party or a large industrial company. If you receive a stipend, you are not getting a contract with the university, but rather small benefits payments from the foundation. They do not count as salary, and have thus different tax implications and potentially some impact e.g. in medical insurance.
The German Academic Exchange Service (DAAD) also provides stipends for German nationals, who want to do their PhD abroad, and for international students who want to do their PhD in Germany.
Research institutions (Max Planck, etc.)
Research positions are also available from research institutions, such as Max Planck institutes, Fraunhofer, Helmholtz, Leibniz institutes. These positions are tied to research projects (institute-funded or via third-party funding). Candidates are employed for such a project and formally need an advisor at a university since the research institutes can't award a PhD. However, actual supervision and advice is provided by the institute, often the head of the institute is a professor, though.
R&D at a commercial company
Some companies (especially the bigger ones like e.g. Bosch) might advertise their own PhD positions. The freedom of research is more limited in these positions compared to universities or research institutions (as the company aims to benefit from the PhD students' work), most of the work contributes to the company, a small share of "own" and publishable research might be allowed. The positions are generally paid well and there are no further requirements like e.g. teaching. A university professor as supervisor is still necessary.
Fachhochschule
The Fachhochschule (FH) or Technische Hochschule – by official translation: university of applied sciences – is a college / polytechnic. They were ranked a step lower than "full" universities in the Diplom times, now they provide (at least on paper) the same BSc and MSc as universities.
Some research positions, typically funded from lab or TA functions or from third-party funding (see above) might be available. Typically, the PhD will be co-supervised with a university, but more and more FHs obtain their own right to defend PhD students. The topics would typically be more applied than at a university.
Above means a PhD candidate from somewhere else wants to start a PhD student position at a FH. Below, we talk about a FH-based MSc, who wants to a PhD.
Depending on the field of study at the FH, (and because of the previous inequality between universities and FHs) if a subsequent PhD is done at a university, a PhD candidate might be required to take some extra courses to make up for the difference in study content between the more applied FH and the more theoretical university. In such a case, the courses which have to be taken, would be individually agreed upon with the supervisor and the university's admission office or similar bodies.

Moonlighting
You might work somewhere else. Maybe some remote job or working part-time. As long as you can finance yourself even independent from the university, you can do a PhD, as long as an agreement of supervision with a professor exists.
Admissions
It makes little sense (at least to me) to blindly apply to a graduate college. Always look for advertised PhD positions or pick a professor and ask them directly. Email and inquiry for an appointment would suffice. It is best if you were a star student in their lectures, but a cold email might work, too.
Attending graduate college might be still an option, but your future supervisor will tell you what is better for you.
Recently, a formal supervision agreements ''(Betreuungsvereinbarung)'' are signed, where goals, time frame, etc. for both sides are listed. Previously (and sometimes still?) the supervision was purely an oral contract. What you as a PhD candidate should get, however, is some kind of the statement from the department, that you are a PhD candidate now. If you are not employed at the university, this might be the only document you have about your relation with it.
If you are employed by the university, you will get a contract. Typically it is about E13 (or some share of it), but that's a separate question.
At some (not all) universities, you can immatriculate (get a student card) as a PhD student. For about 200-300 € per semester, this means similar perks as for regular students, you get cheaper food at mensa, a local bus/train ticket and student price at museums, etc.
Not only professors

Postdocs might have some grants available. Is the supervisor the postdoc or the chair is a question to be discussed.
Habilitation candidates and habilitated faculty members typically have all the rights of a professor concerning supervision of the PhD students. If they have funding available is the crucial question.
Junior-Professoren (basically, assistant professors) are same as professors concerning supervision.

Is a doctoral candidate/student allowed to take courses to fill in gaps?

@Buffy: Good question. In general, nobody at a public university in Germany will prevent a PhD student (or any other student from the university) from attending any lecture about whatever topic the student is interested in. (There is, with few exceptions, no such thing as a fee for individual courses. For many lectures, nobody will even notice who precisely is sitting in the audience.) It's probably a bit more delicate for seminar-like courses, or courses that require the use of (expensive) equipment, for instance since the number of participants for such a course will typically be limited.

Usually, it is easy to find a PhD supervisor, it is harder to find someone willing to pay you. More ways of employment: (1) External research institute like Fraunhofer or Max Plank, (2) company funded research positions, where you work for (say) 80% in R&D and >20% towards your PhD on a related topic, or (3) working on research projects in Fachhochschulen. Usually, such institutes/companies have good connections to nearby universities for official supervision or, in the case of Fachhochschulen, are slowly getting permission to supervise PhD candidates themselves.

@MarkusLange-Hegermann: Thanks, updated!

@Roland: Sure, but I wanted to list all possibilities. Feel free to edit the entry.

@Buffy In some cases PhD candidates are even required to take some additional courses: this is often the case when people with FH-master (applied sciences) are doing their PhD at a "regular" university. If and which courses the PhD candidate must take is indivually agrred upon by supervisor and university admissions office, depending on the courses the student has taken during bachelors and masters.

@Roland: Please edit then. I have less experience with Fraunhofer and Co., but don't they get to sit on their "basically, postdoc" positions more or less forever? This is definitely not the case for universities.

There is a writeup (in German) about possibilities to fund your own PhD: https://www.academics.de/ratgeber/finanzierung-promotion

By "charity", I assume you are referring to Stiftungen. If so, could you perhaps change it to "foundation" or similar? "Charity" very much connotes material aid to the poor, not support for Ph.D. students. For instance, the English-language Wikipedia pages for the Studienstiftung, the Adenauerstiftung and the Cusanuswerk all do not contain the word "charity", but use "foundation" or "sponsorship organization".

United States united-states
Applying
In the US, a doctoral application is normally made to a specific department at a university. The applicant is normally expected to hold at least a bachelors degree or be close to completion. There are rare exceptions to both of these.
An application isn't made to a specific professor, but to a department. Most applicants hold only a bachelors.
Most programs admit students to begin only in the Fall semester. Application deadlines are set by each university. They vary widely, but might be as much as a year ahead of when you'd like to start and aren't likely to be less than six months.  They are usually firm deadlines, though some consideration might be given to one or two late-arriving documents.
The application is handled by a committee of (mostly) professors in the department and follows a defined process that is specific to the university. There is no national system of higher education in the US.
A fee is often required (in the $50-100) range. Universities assess this fee to remove the lowest-effort applications, and it can sometimes be waived for financial hardship; requirements vary by university.
Requirements
The requirements of an application vary a bit, but normally require transcripts from all post secondary (after high-school) education. The transcripts are usually required to be official and come directly from the university (an unofficial copy may be sufficient for applications, with an official version required only upon acceptance; look for specific instructions for the programs you apply to). Copies of diploma certificates are not normally required and will be specified when they are. The GPA will be considered. The GPA in the field will be given higher weight. Some universities, especially those with many applications might have a minimum GPA requirement, but exceeding such a GPA does not mean admission is ensured. The translation of the meaning of GPA from another system is usually (not always) computed by the university.
Letters of recommendation are treated as very important. The committee is trying to make a prediction about the likely success of the applicant, both in study and thereafter. The letters, unlike the CV, therefore, must provide strong evidence of future success, not just past successful activities.
The applicant will normally be asked for a CV, detailing past accomplishments, such as papers written and other activities.
The applicant will normally be asked to provide a written Statement of Purpose (SoP). The SoP should detail future plans, for study and thereafter. It should be somewhat specific (more so for those holding a masters degree), but doesn't need a detailed research plan, nor a topic for dissertation research. It might be enough to name a subfield of the major field. It is not just a recapitulation of the CV, but should focus on the future and how you plan to get there. In particular it should never be used to give excuses for past issues/failures.
Examinations
The GRE exam may be required or not, as may a specialized field exam. This seems to be disappearing at the moment.
For international students, a test of English proficiency is probably required TOEFL or IELTS. And, a visa will also needed eventually, of course.
The applicant might be asked to provide a writing sample. Requirements vary, but it can be, for example, an excerpt from some paper written for coursework. It doesn't normally need to be published work.
There may be an interview required before acceptance. It is more likely to be via Zoom, these days.
Acceptance
The committee normally takes a generalized view, though individuals on the committee may be more interested in some aspects than others. They normally have more applicants than positions available, so the process is competitive; especially so at top ranked universities.
If you are "accepted" into a program then you need to respond to the offer by a certain date. Many US universities are parties to the April 15 Resolution which stipulates that offers of graduate admission and financial support can be accepted or rejected up until April 15 of the year you start study in the Fall. This can vary as it is just a private agreement, not a law or regulation.
Declining
It is not rude in any way to decline before or on April 15 (or whatever deadline). Departments may go down a waiting list if you decline, so your spot is most likely not available if you change your mind. As such, if you are waitlisted, you may be moved off it on or after April 15.
Roughly, you are more like to be moved off a waitlist as programs go down in rank.
Funding
Funding decisions can be separate from applications for study. Many US PhD programs will guarantee funding for an interval sufficient to graduate. However, it is up to the student to graduate during this time and additional work by the student may be required (for example, as a Teaching Assistant). Funding typically comes with a small stipend (sufficient for living expenses for one person) and additionally covers tuition costs.
Programs should describe where funding typically comes from for their students. In some fields most students a funded via a Teaching Assistant (TA) position that requires some number of hours per week in assisting (say, grading) for undergraduate courses. TA positions may be restricted by language proficiency.
In other fields, most funding is as a Research Assistant (RA) provided by individual advisors/professors, usually under an external grant. Such grant funding might depend on grant renewals, but the department might be able to provide a backup (TA) position in case of non-renewal.
Other graduate students may be funded as project assistants or by outside fellowships. Fellowships in the US are most often through an external application to a granting agency, and some international students are funded by their home country (often with a stipulation that they return to work in that country).
It is rare for doctoral students to be self-funded or to pay their own tuition in the US.

Notes:
This answer applies only for doctoral admissions. Masters level admissions can be quite different (or not). In particular, there are many institutions that offer masters degrees but not doctorates, or doctorates only in a small number of fields.
For more details about how to put together a competitive application, see this canonical question.
Caveats
There are exceptions in US to nearly everything here so this is only a general overview. If you are serious about an individual institution you need to explore their published information. Look for websites both by program/degree and more general information for the institution. Again, the US has no national educational system at any level. There are some regulations, however.

Sweden sweden
In many ways, PhD programmes in Sweden are similar to the Dutch and German model, but there are some differences applicants should be aware of.
Note that the following is accurate for academic PhD students. In addition, some departments allow for industrial PhD students, for which much of the below will not be accurate. However, I have found that industrial PhD positions are normally not "offered" to outsiders, but specifically created for individuals, so these positions are probably less interesting to the average reader of this post.
Status of PhD Candidates
PhD students in Sweden have a dual status - they are students with all rights and obligations that come with that status, but they are also full-time employees of the university. In addition to their research, PhD students may be asked to do other work for their employer, usually work as a teaching assistant. This can lead to some friction, and in practice university regulations and Swedish law restricts departments from burdening PhD students with too many distractions.
The job "PhD student" comes with a full salary (fixed through union bargaining), and full employee benefits, including rather generous paid time off. The salary is below comparable industry positions, but not entirely terrible (though opinions will vary).
Some Swedish universities still award a special degree (the "licentiate") as a sort of halfway point during a PhD study. One can leave the program with a licentiate; this is similar to "exiting with a master's" in the US. However, it's normally not possible to be admitted with the explicit goal of leaving with a licentiate.
Advisory Model
Sweden has a different PhD advisory model than most places. Students in Sweden are assigned an entire "supervision team", consisting of:

Main supervisor (typically the professor who acquired the funding)
Secondary supervisor (main and second supervisor are typically working with the student, publishing papers with them and coaching them towards successful completion)
Examiner (mostly responsible for evaluation of progress, signing off coursework, etc.; whereas supervisors are normally supposed to be a student's allies and advocates, an examiner is responsible for quality control and evaluation, and typically is not directly involved in the student's research)
PhD school representative (ensuring that the other three people do their job, ensuring that regulations are being followed, etc.)

The exact "job" of each member of this team is different from group to group and student to student - in some cases, examiners are completely hands-off, in other cases they expect to sign off on all research a student plans to do (and even co-author papers with the student). In some cases the secondary supervisor is a postdoc of the main supervisor (and then in practice acts as the first contact point for the student), in some cases it's a more experienced professor mostly mentoring the main supervisor (but rarely talking to the student directly).
In theory, the model is supposed to provide redundancy and allow students to complete even if they have conflicts with their main supervisor. In practice, the model can lead to difficulties since students can find themselves in a situation where they need to satisfy multiple stakeholders (who don't always have the same priorities, expectations, and needs).
Applying
There is in practice no "applying to a PhD school" in Sweden. Positions are advertised through the university job portal, recruiting tends to follow the same standards that are also being used for other university staff, and admittance to the PhD school comes automatically with being offered a job.
Cold-emailing professors may make a limited amount of sense, but only to inquire if there are currently openings or if openings are likely to appear in the near future. By and large, universities are not able to hire anybody outside of pre-approved hiring procedures.
There are no hiring rounds, positions are advertised one-by-one and on a rolling basis, whenever funding and approval for a hiring becomes available.
As in most places in Europe, a master's degree is a hard requirement. Exceptions can, to the best of my knowledge, not be granted.
There is basically no standardisation of how the application and selection procedure is organised - some groups make decisions quickly based on CVs and a single round of Zoom interviews, whereas other groups run candidates through a gauntlet of multiple rounds of remote or on-site interviews, writing samples, and trial tasks. However, there are no application fees.
Requirements
PhD candidates require a relevant master's degree and typically need to be fluent in English. Swedish is, at least in STEM, generally not required, and there tends to be no requirement to ever learn Swedish.
Aside from that, the job profile ("kravprofil") will list what other competencies are required or recommended. How undergrad grades, prior experience, writing samples, etc. are weighted will depend heavily on the professor doing the selection, and very little can be said in general about this.
This means that even "unusual" candidates have a chance to be selected, if they happen to run into the right kind of professor with the right kind of requirements.
Acceptance
"Acceptance" is generally communicated rather informally, via telephone or through a short "congratulations" email. There are no formal offer letters like in other countries. However, Swedish universities (at least research-intensive ones) are used to applicants from outside the European Union, and should be able to quickly produce the documentation necessary to apply for a student visa (despite being full-time employees, PhD students count as "students" in front of the migration office, and hence a student visa is required rather than a work permit - this does not prevent employment by the university).
Note that by law universities can only actually sign a contract with students who are physically in Sweden. International students get a written "contract promise" which is sufficient for a visa, but EU applications basically only get an email and get informed to move to Sweden and then get their contract. This often feels informal and weird to candidates, but is indeed the intended practice.
It's difficult to say how long the procedure takes because it depends heavily on the professor doing the hiring, but in general the process is rather fast-moving - acceptance and rejection notices are typically sent out reasonably quickly (or, at least, most professors are fairly transparent with where the process currently is).
Funding
Positions in Sweden are fully funded by Swedish law. Universities are not able to offer "part-time" positions, or accept self-funded students (the only exception are industrial PhD students, where somebody else still needs to provide full-time funding).
Notably, universities are required to provide funding at least for the "normal" duration of a PhD. This is typically 4 years, but can be defined differently in different departments. For instance, in my Computer Science department, normal PhD time is 5 years (including 20% teaching obligations). It is in principle possible to be let go as a student for performance reasons, but in practice this barely ever seems to happen (at least not in my department). You can safely assume that if you get a PhD position, you will be fully funded as long as stay within a reasonable PhD duration.

France france
Note: I did my PhD in France 2012 - 2016, but then continued my academic career in the UK. So some of this might be outdated, a narrow picture, or use incorrect terminology.
Funding availability
Advisors may advertise potential PhD topics on their institutional web pages before any funding has been secured. It indicates that they have considered the topic, fleshed out a PhD project, and considered funding sources to apply to.
This is due to the fact that PhD funding is awarded, by many funding sources, not just to a potential advisor on a topic, but to a specific advisor and a specific student on a specific topic. The potential PhD candidate needs to be known for the application process, and is more or less involved in it.
I am also aware that many of my colleagues have had PhD positions supported through industry collaborations; however I am now aware how and at which point these are funded and advertised.
Qualifications required
The only "required" qualification is a Masters diploma in an appropriate field. However, as the applicant is essentially applying for funding together with their potential supervisor, and may even be required to present the project proposal themselves (see next section), most successful applicants will have a strong prior knowledge in some part of their PhD topic (mine was a combination of a research area I was familiar with from my Masters, and a completely new field). This typically means more than would be covered in regular coursework.
Fluency in French is obviously a massive advantage to any applicant. But, it is not a requirement (I finally started being able to communicate in French in my last PhD year - and promptly forgot most of it when I left).
I am not aware of any restrictions on the nationality/origins of the applicant; I was neither a French nor an EU citizen while applying and it didn't seem to get brought up at all. In fact, the PhD students employed by my lab were of extremely diverse origins.
The application process
As mentioned above, the potential PhD candidate will apply for funding together with their advisor. It is therefore crucial to establish contact with potential advisors well in advance. If there is mutual interest, the advisors will tailor the application to the student's CV. In case of a formal interview process, they will also coach the applicant during the preparation for the interview.
We have applied to two funding sources. One was French government funding, which I'll elaborate on -- this is where we applied with the original project for which I contacted the advisors, and prepared the most. My advisors have also put together an alternative application to a different funding body, tweaking the original proposal somewhat into a very related topic. This alternative was a written-only application, requiring no effort from me as an applicant.
The application for French government funding included an interview in front of a scientific panel with broad expertise (so, not topic-specific). The student applicant is expected to present the project, briefly review the state-of-the-art, and describe the research ideas they would be pursuing. This part of the process is what makes is essential to establish prior contact with potential advisors -- as they will be able to provide materials to prepare for the interview and put together a presentation.
While I have not personally attempted this myself, this also indicates that a potential candidate with an extremely good fit to the research topic of an advisor might be able to apply for a position without the advisor advertising a specific project previously. If the applicant had contacted the potential advisor well in advance, got their interest and established common research interests, a project may be tailored together with the student before an application to a funding body.
Both of the applications processes resulted in a ranked list of applicants, where the number of positions to be funded was made known in advance. After these are published, any candidates that are "in the funding" can make the choice to either accept or reject the funding -- rejections do happen as some candidates might have applied to, and got accepted by, different funding bodies. The candidates that did not make the cut, but were close to it, should still be monitoring the results for a few weeks until all the conflicts and double applications resolve, as it is possible for them to still make the cut after better ranked applicants make their final choices.
Another detail to point out is the role of academic internships in the PhD application process. While they are by no means a requirement, securing a semester-long or a summer research internship with a French advisor is a very common way for potential PhD students to find PhD positions, and the advisors to find potential students. It is often regarded as a "trial run" or an unofficial probation for both parties. A large proportion of internships end in a PhD offer. These can be fully or partially funded sufficiently to scrape by, but not glamorously paid by any means. An additional advantage is that it also puts the potential PhD candidate in a position where they can reach out to a much larger pool of potential advisors in person, rather than through e-mail.
Format of study, status of applicant
French PhD students are somewhat stuck in limbo. They have an official student card (which can be frequently used for various discounted tickets and services), but they are also officially employed by their research institute.
The PhD candidates will therefore receive a regular salary, which is not standardised (unlike some other places), and will depend on the funding source supporting the position. The French government grants resulted in the lowest salaries (but were considered some of the more secure funding), but were generally enough to get by in a decidedly unglamorous but very lively student lifestyle. The candidates are expected to pay for the yearly tuition themselves, but this was quite a low amount (around €400/year; which I could begrudgingly cover from my PhD salary).
While not affecting the candidate too much, the institutions are organised in such a way that research labs provide teaching to the University (the services provided by permanent academics), while the University agrees to issue diplomas to their PhD students. Typically a PhD student will actually have very little contact with the University issuing their diploma, and will work in the research institute.
Most funding is available for a strict period of 3 years. Extensions of 1-3 months might be possible through applying for further funding, but I remember they were becoming less available as I was leaving. Due to certain French employment protection laws, it is extremely unlikely that the research lab would offer the candidate an alternative position while finishing their PhD (outside the above mentioned extensions) so finishing within 3 years is a very strong target. If planning to continue the academic career in France, a PhD taking longer than 3 years plus a few months will raise some eyebrows.
When I did my PhD, PhD positions either included certain teaching/TAing requirements, or none at all. (Teaching contracts obviously paid extra; but were nearly impossible to secure without being fluent in French) However, both PhD students and advisors were not particularly happy with the system (full-teaching contracts were not very desirable as teaching requirements were quite high, while the non-teaching students who wanted some experience teaching could not actually get any teaching), so I'm not sure whether the system changed at all in the meantime.
An additional detail for consideration, while more related to the end of the PhD than the application process, which can potentially influence the choice of applying for a PhD in France, is the candidates status after graduating / after the funding runs out. France has a very accommodating social system, which has been adjusted to keep the talent in. As PhD students are employed, they are eligible to receive generous unemployment benefits following the end of their PhD contract. This is also true for international/non-EU students (thought the period is shorter). This means that after finishing their PhD in France, the new Doctors are not forced to scramble for their next position while preparing their viva, and are not kicked out of the country the day after their defence, but are in fact granted a grace period following their completion in which they can look for and interview for their next position.
Choice of research topic and advisor
Prior contact with the advisor and detailed discussions on the topic are crucial before an application to a funding body. A potential advisor will personally work with their preferred applicant in preparing the funding proposal for the position.
As mentioned in the paragraph on qualifications, the candidate is expected to have the knowledge of, and experience with using, the state-of-the-art approaches from the area of research of their potential PhD. Therefore, for contacting potential advisors, I would strongly suggest highlighting specific mutual research interests and your specific and relevant experience, rather than just indicating a general interest in the potential advisor or their research.

Japan japan
This community wiki answer was synthesized from other answers across the site, especially this answer about finding advisors and this one about the Kenkyusei option. Please feel free to edit this answer to improve it.
Application Pathways
The main question is whether you speak Japanese well enough to take classes and do research.

If you do, you can look for openings on departmental websites and reach out to professors.
If you do not, your best bet is to apply for fellowships that specifically cater to foreign students. The MEXT scholarship is the most common option. Some of these programs will allow you to study in English, but some may require you to study Japanese (and living in Japan without speaking Japanese is somewhat more difficult than the analogous situation in Europe).

Most Japanese grad programs are three years and require a master's degree, but a few are five years and require only a bachelor's.
Kenkyusei (Research Student Positions) and the Grad School Entrance Exam
Most grad programs have an entrance exam that must be passed before you can enroll. These exams may, or may not, be available in English. If you are already in a position to pass the exam, and are financially able to physically take the exam in Japan, you can take it and attempt to enroll in a PhD program directly.
However, many students (and most foreigners) spend some time as a "kenkyusei" (research student) before enrolling in their degree program. Kenkyusei allows you to do some research under the supervision of a professor (ideally the one who would advise you as a PhD), taking Japanese classes and more broadly getting adjusted to your new environment while preparing for the university's PhD entrance exam. Most foreign students on Government scholarships will spend their first year as a research student.
As a research student, your exact activities and responsibilities must be negotiated with your supervisor. In particular, "research student" is a bit of a misnomer; it is likely that you will have no research responsibilities (or opportunities) and your only activity will be studying for the exam.
Finding an advisor (usually required for admission)
You will usually need an advisor lined up before you can start studying. Even if you win a MEXT scholarship without an advisor lined up, your first job will be to find an advisor.
There's several things to consider in terms of how to contact people.

You need to search Japanese university websites in your field. This is going to be nearly impossible if you don't have any Japanese fluency.
Then you're going to want to find researchers who you could imagine working with presumably you'd narrow it in terms of both research interest and their ability to use languages you can use (e.g., English).
Write them a letter explaining you are receiving a scholarship from the Monkasho (文部科学省) and would like to study in their university, starting from being a kenkyuusei (研究生).
See who responds.

As a basic rule, you are more likely to get a response from professors at universities that are used to hosting international students with MEXT scholarships. This will mean national universities like: Tokyo University, Kyoto University, Tohoku University, Kyuusyuu University, Hokkaido University, Nagoya University, Hitotsubashi, etc. and well-known private universities like Waseda, ICU, Keio, Aoyama.
More minor schools (prefectural or city ones) will probably not be super familiar with the procedures and would require strong support and interest from the advisor -- who doesn't get much time or money to help work on this (and it's quite the administrative hassle).
Separately, Japan is a place where knowing people is more than half the battle so it's hard to build connections from scratch. Instead, you're hoping that at least one person will respond and either be open to hosting your or know someone who is that they are willing to forward your e-mail to.
Other Considerations

The Japanese academic year starts in April. This can be difficult for Western students (though it works out well if you do the kenkyusei period).
Japanese academia, like Japanese culture more generally, is significantly different than Western culture. In particular, the hierarchy is relatively strict and students are usually extremely respectful and deferential to professors. Similarly, Japanese is one of the most difficult languages to learn (for native Indo-European speakers).
As an outsider, the (sometimes very significant) differences between the prestige of different Japanese universities may be difficult to ascertain. (However, those evaluating your credentials will likely content with the same opacity, if you return to the West post-PhD).
While Japan is known for a brutal work-life balance, this is more an issue in private companies than in universities. Many grad students report not being expected to work weekends.

England (and the UK) uk
Note: I assume the process is somewhat similar through the UK, but I know there are some difference between the four constituent countries. I am mostly familiar with the situation in England.
Note 2: I work in computer science / robotics so if anybody is aware of differences to other areas, please do edit them in.
Funding Availability
Broadly speaking, there are two types: institutional and individual.
The UK PhD funding has been leaning towards large institutional grants for "PhD programmes" spanning several cohorts and away from funding for individual positions. Such funding might support e.g. 5 (new) PhD students in a certain research area (e.g. "FoodBioSystems", "Agricultural Robotics") for 3-4 years. These positions will therefore usually be advertised in more general terms related to the overarching goals of the research area (i.e. "Increase automation in food production to support environmentally friendly agricultural practices"), rather than describing a specific PhD project.
In recent years, one increasingly sees the funded CDT (=Center for Doctoral Training) doctorates advertised with strict timelines and formalised processes.
Individual positions still do exist, but are much less frequent. These are advertised by an individual advisor (or advisors) and describe a specific project the candidate would be working on.
It is not uncommon to see an individual supervisor (advisor) advertising individual research projects under the category of self-funded: these do not come with expectations of funding. They are more suited for individuals having some form of funding (home country scholarship/funding) or personal funding.
It is important to note that many of these funded PhD positions have international student "quotas" in some form or another. The institutional programmes might only be allowed to admit up to 20% of international students for the duration of the programme. Some individual PhD funding may only cover domestic student fees, making the position essentially unfunded for international students. In such instance, the international student is expected to pay the difference between the 'home' tuition fee and the international tuition fee by themselves.
Qualifications required
On paper, most (all?) of the PhD positions only require the applicant with a Bachelors degree or an equivalent. This is further reinforced as most institutional PhD programmes are in fact a 1+3 year programmes with an integrated Masters year.
However, due to the above situation with international "quotas", funded positions open to everybody tend to be much more competitive than the domestic-only positions, and it is not uncommon for most applicants to actually hold a Masters degree prior to applying.
The application process
As most positions are supported through doctoral programmes, they are somewhat seasonal. The applications for the coming academic year (starting September/October) would close around March time, the previous academic year. The timing is not so strict for students bringing their own funding (self-funded or otherwise).
Prior contact with a potential supervisor is less crucial when applying to an institutional doctoral programme, as the potential PhD projects for the incoming cohort might still not be fully planned or approved -- but you can (and should) look at the research profiles of the academics involved in the programme.
If the position concerns a specific project, contacting the potential advisor in advance might provide very valuable details to both parties, both about the topic, expected/provided style of supervision, etc.
In both cases the application process will have two stages:

The online application form is usually fairly structured and broken down into a series of questions. Think of these as a series of mini-cover-letters, where the topic of each is highlighted by the question. You can also enclose a "real" cover letter, a CV and (possibly required?) your transcripts.
A panel will examine this and determine a shortlist of candidates to interview. The number of candidates to interview for a single position is not predetermined; the panel will balance their time and effort invested in interviewing with how promising the candidate pool is. Around 3-6 candidates may be invited for the interview.

The interview panel will typically consist of around 3 academics and a non-research person. For individual, you might have 2 academics depending on the discipline and faculty.
Panel diversity is usually enforced by the Universities.
These will last around 30 minutes (to an hour maybe?); again with a series of questions to the candidate and an opportunity for the candidate to ask any questions of their own in the end. Some questions will be application-specific, related to either technical or practical skills related to the PhD. Usually 1-3 questions will be very standard and you can easily search around for lists of these types of questions ("What motivated you to apply to this position") and some strategies to answering them.

For the individual positions, the decision is reached very quickly. The candidates are ranked based on the interview, and the first candidate will be contacted within a couple of days, with the hopes of getting an decision from the candidate fairly quickly. Most advisors would be happy to wait for up to a week, but may or may not be open to waiting for longer. The position would be offered to the next-ranked candidate if the first one turns it down, and so on until somebody accepts or the position has been offered to all candidates found acceptable during the interviews.
I am honestly not 100% sure of the timeline for the positions supported through doctoral programmes, but I would say it is likely very similar, with potentially a slightly longer delay between the interviews and making the offer to the best candidate.
Format of study, status of the candidate
The institutional doctoral programmes are typically a 1+3 years programmes, with the first year being a taught Masters degree (with coursework: discipline and/or research courses).
The individual ones are typically simply 3 years long research positions.
In both cases, the candidate will in fact start as a Master student (thought / by research), and will be required to make a "PhD transfer" following their first year. Some will offer a MPhil which would be upgraded to the PhD after 'good' progress.
During the whole PhD, the candidate is considered a student, and will not be paid a salary (taxable income) but rather a bursary/stipend (non-taxable). This is a fixed, prescribed amount for all the students, which will get reviewed (typically very slightly increased to account for inflation) on a yearly basis. Some students (at "proper" PhD level) may be required to, or asked to, serve as TAs/demonstrators in practical workshops, which may or may not be paid, but is typically neither a big time requirement nor a large sum of money.
Choice of research topic and advisor
With individual positions, the advisor will be involved in reviewing the applications as well as interviewing. The topic will be known in advance and advertised. A successful candidate will start working on this topic from the start of their PhD.
For institutional doctoral programmes, the topic and advisor may not be chosen until the end of the first (Masters) year. Typically, the student starts to work towards it in the course of the first year.
A set of available topics and advisors would be presented to the students through this year, both formally and informally through any contact with the potential advisors that was established through the year (e.g. from coursework). The first focused work on the topic related to the PhD would typically be the final project in the 'MSc year'.
There may be some opportunities for the students themselves to be involved in formulating the projects/topics, especially during their Masters year. However, PhD projects are accepted to be fairly flexible, and should be tailored to the students interests as they progress.
An industry partner may also be involved in some capacity in the PhD project. This is increasingly true for the institutional doctoral programmes, as there is a push to increase the collaboration between academia and industry. This is especially true where institutions offer professional doctorates: DEng, DEd.
Professional doctorates (such as DEng, DEd, DBA) are structured doctorates with cohort training and research.
Thesis
Thesis can take the form of the traditional thesis where the student writes up chapters and follows a suggested word length.
Thesis by article is gaining traction (think of PhD by Publication).
For noting: There's the PhD by Publication (retrospective route) which does not fall under the institution and individual explained here. This is for researchers with research publications in their field and would like to formalise their experience by gaining a PhD. The application process is case-by-case and follows eligibility criteria in the Academic Regulations. A variant is the PhD by Practice which formalise prior notable works (arts, exhibition, literary...).

Italy italy
Requirements
As is usual in Europe, candidates must already have a Bologna-process master's degree or equivalent title (or be about to obtain one: often having defended one's thesis is not necessary at the moment of application).
Admission process
Each department opens a number of PhD positions. The exact regulations vary across universities and fields, but usually having a contact with a professor at the institution and a specific research project is not necessary to apply. The students can freely choose who they wish to work with after being admitted.
Traditionally, admission deadlines are around August/September, so that the winners can start their PhD later in the year (around October/November), but recently universities have started opening additional calls earlier in Spring, in the hope to beat the competition on time and get better students.
Duration, obligations, and funding
Positions are funded for 3-4 years, and the degree must be obtained before the end of the fourth year, barring extraordinary circumstances. It is not mandatory to teach during one's course, but it is often welcome and it is a way to get a little extra money.
Often the students are required to spend a few months abroad during the duration of their program to collaborate with other research institutes, and additional funds are allocated to cover for this research stay.
Most positions come with a stipend, but a certain number of runners-up is admitted to a position without funding (dottorato senza borsa). It is needless to say that these are not a good proposition, unless someone has a different way to support themselves or obtain funding. A common case is that of school teachers and other Italian public-sector employees, who can get a paid leave to study for a PhD.
Project-specific positions
Less than half of the positions (depending on the field and the department) are on specific research projects that allocated funding for them. Nevertheless, the admissions still go through the department, not through the PI.
How to find positions and apply
Openings are advertised on the university's website, and sometimes professors post them on field-specific mailing lists. There is little point in sending cold e-mails to individual professors to inquire for positions, since they cannot hire students directly.

Russia russia
Overview
In Russia, the experience of applying for PhD programs differs quite dramatically between domestic and international students, the latter being almost non-existent until fairly recently. International students mostly apply for positions specifically created for them and this quota is therefore separate from that of the domestic applicants; what these programs entail is very much a case-by-case basis, although some general information will be offered to the best of my knowledge.
On the whole, in Russia, PhD studies are detached from becoming a PhD. One may become a PhD without ever being a PhD student and one may finish doctorate studies without ever becoming a PhD. This quirk means the incentive to enroll is quite weak. There is, however, a perverse incentive: being a domestic full-time PhD student means having conscription immunity. Needless to say, PhD students are disproportionately male as compared to MSc graduates.
Post-graduate job market is extremely heterogeneous as well. At the time of writing, the vast majority of fresh graduates either moves abroad or quits academia. For the former, the ex-student might expect a LoR but not really any more help, unless the lab is well-connected internationally - not many are.
Overall I would say that while BSc and MSc education is traditionally strong in Russia and the skills one would get are reasonably marketable, PhD studies are crippled by the severe underfunding of science. Even though some labs have gotten top-notch equipment, this is far from universal and has happened recently enough that the complaint about the capacity to operate said equipment is far too common. Again, fields and subfields may differ drastically: Russians are big on intellectual traditions, and some schools of thought and labs are still very much alive. This has to be assessed individually.
PhD program options
There are several significantly different options for PhD programs in Russia. The positions may be state-funded or have tuition fees, the education may be full-time or take a form of correspondence studies. Tuition fees typically range from $1500 to $5000 yearly, this option attracts not insignificant amount of applicants yearly and universities pose very little extra requirements for those opting for it.
In recent years, quite a lot of new options for foreign students have emerged, most notably the 5-100 program (wiki). It is explicitly aimed at the increase of the fraction of international students and professors, and decently funded positions are created.
This is, however, entirely detached from the rest of the academic experience in Russia. No regular rules apply there, and it operates entirely on a case-by-case basis. For this quite possibly the most significant scenario of a foreign student getting into a PhD program in Russia, studying the specific terms is much required and offering any general guidance is nigh impossible.
Status of PhD Candidates
In Russia, PhD candidates are considered students. The program lasts for 3-5 years and, for domestic students, does not end with the PhD thesis defense - rather, they submit a "final project" for evaluation. These projects are intended to be a ready-to-submit theses; however, at the time of writing, the conversion rate is below 10%. Before the federal law change in late 2012, the successful end of the PhD program was marked by a thesis defense, but this is no longer the case, and the rate of actual defenses taking place at the end of the program has plummeted ever since.
Other than that, the importance of being a PhD student rather than a regular lab employee boils down to the advisor getting compensated for the supervision and providing help with the thesis writing/submission rather than just the subject area of PhD studies. Another thing worth mentioning is the university-provided dormitory, which is important for many foreign students coming primarily from CIS countries because of their financial situation - more well-to-do students, however, generally prefer to rent instead.
Funding
Funding is a sore spot, and understanding it is required for understanding the rest of the answer. PhD students are financed, but it is utterly insufficient for living: the stipend is on the scale of $100 monthly. Therefore, three major ways of funding have emerged:

Regular research grants. With some senior member of the lab being the PI, the student then becomes a salaried employee for the duration of said research grant. Given how winning the grant in March commonly means the grant agency starting to transfer funds no earlier than September/October/November, it can be a massively painful experience - thankfully, it is expected that the supervisor/PI would sort it out with the university and the funding agency.
"Personal" grants. PhD students are eligible for participating in small-scale student grant competitions offering up to the far more sensible $1000 monthly or so. These grants are few and not many even bother participating, but it is nonetheless a viable venue.
External funding. It may be working for a company (sometimes having nothing to do with the research topic), financial help from the family or, in case of foreign students, their own government's financing.

Most commonly, they are mixed and matched. For the reasons outside the scope of this answer, enlisting a student in multiple grants for tiny income from each is an ordinary practice. It is also fairly rare for students to not get any external funding at all: most of them would either get support from relatives or work on the side. In a sense, the latter is expected by the government: students from single-parent families are eligible for an additional $150 or so monthly as a so-called "social" stipend.
This all means that the supervisor capacity is not really a limiting factor here, most advisors would not think twice about taking in someone who is not completely useless if they work for free :) While there may still be some frustration with the academic performance of the PhD student, the entire arrangement is commonly viewed through the lens of "is this person worth spending my time and grant money on".
Requirements
The MSc degree is a hard requirement. There are also exams to be passed which vary by position/university, but normally it is speciality (see below), English, and philosophy. For foreign students, a Russian proficiency exam is common: very few programs are taught in English exclusively. Oftentimes, some prior certifications are provided instead: if the student obtained their MSc from the same university, they would have taken these exams during MSc studies. Transcripts from other universities are generally accepted, but this is not a hard rule.
Applying
Another sidetracking preface for the following two sections: Nearly everything in Russia gets done "behind the scenes", and formal proceedings are merely a façade for it. The main reason for this is bureaucracy: every single correction entering the official channel takes weeks if not months of back-and-forth exchange between several organizations, so the usual practice would be all parties agreeing on a course of action  and fulfilling their obligations first and only then signing relevant papers.
In Russia, it is common for MSc's to enroll into a PhD program at the same university they have graduated, often with the same supervisor as well. In fact, it is even encouraged, as their work in this new capacity is perceived as returning on the initial investment their supervisors made while educating them before. Exchange terms abroad are also encouraged and changing fields/supervisors/taking a break before the PhD are quite ubiquitous, yet the "ideal" process would be just working in the same lab from the sophomore year or so on and on.
With all that context established, it is now clear that "cold" applications are very rare and people treat them with suspicion. This is not to say the committee would act in bad faith or the applicants would be treated unfairly, rather that there should be a convincing reason to apply for the program in the first place, and without any kind of prior collaboration or recommendations from the previous supervisor or professors that is virtually unheard of. To that end, the agreement with the future supervisor shall be reached before the formal admittance, with very few exceptions.
The application itself requires transcripts and an affirmation one holds the MSc degree or equivalent. As customary in Russia, the checklist goes on to include another half a dozen positions, ranging from the ID scans/copies and the health certificate to photos. In general, though, there is nothing terribly complicated about those, aside for the student visa for foreign students.
There will be a brief on-site interview with the faculty, this stage is important and functionally combines presenting the statement of purpose and the CV. One should not stress out too much about it, however: at this stage the future supervisor pretty much already vouches for them if the prior arrangements were made as they should have been. Essentially, one should treat the application process as convincing their future supervisor and then going through the formalities.
PhD studies and thesis defense
During the PhD program, students take courses in English and philosophy yet again and pass their candidate exams at the end of the first year. They also are normally required to have a bit of teaching duties, and it can take many forms, one common option is being a TA for a year (~50 hours). After that, in a typical PhD program, they focus solely on research.
Thesis defense is also a bit unusual and worth a separate mention.
Every program has a research field called speciality associated with it (in rare cases, several at once); Russia uses its own nomenclature, which changes quite often - the latest revision is about a year old at the time of writing. Some universities have the thesis committee corresponding to that speciality in-house, others do not - having the in-house one makes submitting the thesis a whole lot easier. Changing one's speciality is a bit of a hassle (not too terrible though) and the speciality itself is frequently overlooked until the very end, yet crucial for the successful thesis defense. The reason for this is that the thesis has to be tailored towards the speciality: it needs to include a list of results, and every point from that list of results has to match one of the (broad) options in the official description of the speciality. Sometimes candidates find out another speciality matches their work better, and that requires retaking the corresponding exam, causing near-inevitable delays.
Another particularity is having to provide about 20 pages long abstract of the thesis, which arguably holds more significance than the thesis itself. Writing a good abstract is hard, and it will be the main document the thesis committee itself is concerned with - the full text is mostly for the opponents to comment on.
As you should already know by now, by the time the defense itself is scheduled, getting a degree is almost a done deal. This is achieved by having a pre-defense hearing of the talk, which is a rehearsal of the "main event". In other words, it is a go/no go meeting.

This body needs to approve the thesis.

Australia australia
Understanding Honours in the Australian system
The Australian system has something called "honors," which is a little confusing. In general, an undergraduate degree in Australia is three years, but you can stay for a fourth ("honors") year that will usually entail both coursework and a research project, leading to a thesis. In some cases, this is equivalent to (or is) a master's degree; in others, this may be integrated into the three-year undergraduate curriculum. Honors degrees come in classes:

first class
second class division A
second class division B
third class

Note that this is different than the British system, where honors are mostly based on grades.
This is important because an honors or master's degree (or, for foreign students, an equivalent demonstration of research ability) is usually required for admission to PhD programs
Requirements for PhD admission
Each university has their own requirements, but in general, the criteria are grades and research:

If you have first class honors, you will be a strong candidate for PhD programs (though there will still be competition; lots of people have first class honors).
If you have second class, division A honors, then you are likely eligible for admission, though your application will be stronger if you have good grades, additional research experience, and good letters of recommendation
Otherwise, you will likely need to obtain a research-based master's degree "performed at a high academic standard" or "an equivalent qualification that demonstrates research experience, excellence, and capability" (as phrased by the University of Sydney).

You will also need to speak English well.
Admissions Process
Australia is a little different than the US or Europe. As in Europe, you will usually need to find an advisor. However, your university may have instructions for how to do this. For example, the University of Sydney has a dedicated matchmaking service, while the University of Melbourne tells you to use e-mail, but has a list of what you should include in this e-mail. Other universities may tell you that finding a supervisor is optional, but in practice, you are much more likely to be admitted if you find a supervisor yourself.
We emphasize that you should carefully craft your letter to prospective supervisors. Supervisors receive many such letters a day, so only ones that are clearly well-targeted and highly personalized are likely to receive a reply.
After finding a supervisor, you still have to get admitted to the university. Your language skills and "marks" (not called GPA in Australia) matter here. "These decisions are based on a threshold, not based on who else applies."
Funding
"Some supervisors have funding they can use to pay PhD students at their discretion, but most PhD students are funded through a university program. The fact that a position has been advertised does not mean the supervisor necessarily has funding for that position." [source]. Rather, the professor-student team will jointly apply for one of the university's funded studentships. There are a fixed number of such studentships, so this is a competitive process.
You may be eligible to be a "tutor" (TA) or to take another position within the department to make money. Your advisor may be able to help you apply for this.
You may also be able to find funding through a government scholarship such as this one.
We emphasize that the stipends, relative to the cost of living in Australia, are quite low compared to Europe or the US. Past users here have reported that "it is a struggle at the best of times." Many students do take outside work to supplement their stipends, but there are strict rules about this, and it's hard to find employment in Australia. Hence, even if you are willing to work outside the university, you will probably need a stipend/scholarship and a fee waiver just to get by; it will be pretty much impossible to survive with only a fee waiver unless you are independently wealthy.
International students
Australian universities routinely deal with international students and will be able to assess foreign credentials. Foreign students will need to apply for a visa. Note that some programs (especially part-time programs) may not be offered to international students, and that international students will need to speak English at a very high level to be admitted.

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Post-doc Salary in Germany
I noticed that there are some significant variation in the salary of post-docs in Germany. The post-doc salary could be given in TVL13, TVL14, TVL15, and even TVL15U scales. This means that the net income could change from 2,000-4,000 Euros. I have currently an offer to start my post-doc with TVL-13 (Stufe 4) which gives a net income of 2,900 Euro. Is this something reasonable?  What factors are important in determining the post-doc salary? and how could I change them?

Postdoc salary (like for any non-tenured academic position) in Germany is fairly rigidly structured. The salary is always according to the federal wage agreement ("Tarifvertrag der Länder", TV-L) and is determined by

pay scale ("Entgeltgruppe"), which depends on the position, in particular, the responsibilities that are officially attached to it. (Basically, no formal responsibility means TV-L E13; responsibility for crucial infrastructure, e.g., running a big device or doing a specific analysis for all the group, means TV-L E14, and being head of a sizeable group means TV-L E15)
pay grade ("Stufe"), which depends on how many years you've had this job (think automatic promotion); you start at Stufe 1, after 1 year you move to Stufe 2, after 2 more years it's Stufe 3 and so on.
percentage of working week ("Wochenarbeitszeit"), which is just what it sounds like. (A full working week is about 40 hours.)
federal state ("Tarifgebiet") of the institution, because the former Western states have a different agreement than the former Eastern states. (Eastern states have lower salary, because the cost of living is (assumed to be) lower.)

Only the second point actually depends on the applicant, the rest is tied to the position and needs to be fixed before it is even announced (e.g., as a 75% TV-L E13 position) and is therefore non-negotiable. The second point is somewhat negotiable by trying to get them to recognize previous postdoc positions with similar responsibility as time on the job (although that is an administrative matter, and the possible influence of the academic staff on the administration varies wildly...)
Which pay scale and in particular percentage is reasonable is very discipline-specific. If it's a full-time position with no responsibilities (such as running critical experiments for everyone else), it seems not bad because Stufe 4 is actually comparatively high (E13 only has five grades).
If you want to get gross and net salaries from pay scale, grade and percentage, you can look it up at http://oeffentlicher-dienst.info (in German, this answer might help navigating the site).

One addition, since Mojtaba mentioned E15Ü: Ü scales exist for the benefit of people who were employed prior to the current scheme, who would otherwise have had a pay cut. New contracts are never issued with an Ü scale.

Worth noting is that the federal state of Hesse (with cities including Frankfurt/Main, Marburg, Gießen and Kassel) has its own salary agreement, the TV-H.

From my experience working 4 years in Germany, I can tell you that you got a reasonable deal. I don't know about those 2900, but at least in the Hamburg region that would be around 2500 Euros net.
You can check the values of 2015 (and beginning of 2016) here.
The TV13 is the standard position for researchers (Wissenschaftlicher Mitarbeiter), which is basically the same as the PhD students, but a higher "Stufe" because of your years of experience. If you manage to get some special responsibility or lead a small group of students ("group leader"), it could be possible to upgrade it to TV14, but that depends on your group leader.

TVL-13 is AFAIK non-negotiable. It sufficies to cover your costs and the costs of your spouse/partner even if you live in the top cities such as Frankfurt, Munich, or Freiburg.
A net income of 2900 € is well within the range of what you could get.
Now, if you'd like to re-calucate it, beware that fighting your way through the regulations, laws and formulas could easily take you about a full week of time. Personally, I've never heard of any single case when the university miscalculated your salary; moreover, it is not your mentor who manages your salary, but special administarion people from the university.

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What if a lecturer has to use the bathroom while on stage?
If a student has to use the bathroom, s/he may simply politely and quietly excuse him/herself for a few minutes.
But is there any established etiquette for what an instructor is to do when nature suddenly calls?  Let's say this is a typical classroom lecture of about 90 minutes, meaning a student body of about 80-90 and no scheduled breaks.
Oh, also, let's assume that there's no real illness or other crippling circumstance that forces the instructor to leave; just a good old-fashioned porcelain inspection, resulting from consuming just a bit much V8 an hour earlier (seriously, that strawberry-banana V-Fusion is addictive).

Give the students an exercise. "Discuss this problem with the person sitting next to you. I'll be back in five minutes."

Part of the usual etiquette is taking off the microphone, if any.

Restroom before class.  In 20 years of teaching, I've never had to leave a class for the restroom.  (I did once become sufficiently ill to need an ambulance.  I said, "Ladies and gentlemen, please excuse me; I am ill.  Class is dismissed," and fled out the door.)

Whatever you do, do NOT wait till the last second. Once I did and had to sprint out of the classroom before I could say "I'll be back". Of course, everyone understood what was up because I got covered in sweat and had a roll of "emergency paper" in my hand while running. It could have ended even worse...

I teach a 3.5 hour night class some terms. For a marathon like that you call breaks. The students need them every bit as much as you do. And you use the facilities during the breaks just like you use them before a normal class.

If you can't hold it in for just 90 minutes then you might consider going to see your doctor. Nature does not usually "suddenly call" - you know when you ate, and you know when you drank, and you know where the restroom is before you step foot into the lecture hall. Unless you avoided going for a wee for several hours before the lecture despite feeling that you needed to, and subsequently drank lots of water, you should be fine for 90 minutes..

I agree with @dmckee. Even if there is no scheduled break, I don't see why you could not make an unscheduled break (a very short one). Staying focused for 90 minutes is nigh-impossible even without bathroom emergencies, and making a short break at the right moment is good for everyone.

@LightnessRacesinOrbit You shouldn't forget that some people suffer from intestinal diseases, as Crohn's Disease or Ulcerative Colitis. It is not a matter of "see your doctor". Maybe the person already did, and it now has a diagnosis and a treatment, but not a cure. So, yes, nature usually "suddenly call" some people. It is not reasonable that those people cannot give a lecture just because that need for a break might happen.

@RafaelEyng: Yes, precisely. I'm saying, if someone thinks this is "normal" then they should go see their doctor, because they may have one of those diseases.

@LightnessRacesinOrbit Many people have to go to the restrooms more frequently because they have to take drugs like diuretics because they suffer from high-blood pressure, and sometimes they have no other options (e.g. because of allergies). Thus, don't be too quick on drawing conclusions on when someone should be fine.

@MassimoOrtolano: You're not listening to me. I'm saying, if you find you can't get through a 90 minute lecture, and you don't already have a known medical reason for it, you need to see a doctor because you may have a medical reason that needs diagnosis. I'm not "drawing conclusions" on anyone. Obviously if you already have special medical needs then that doesn't apply.

@LightnessRacesinOrbit I agree, thank you for the clarification.

@MassimoOrtolano: :)

It is nothing to be ashamed about.  Everybody poops.  Give your students a break and take care of your biological needs.  http://www.amazon.com/Everyone-Turtleback-Library-Binding-Edition/dp/0613685725

"Intermission" back in 10 minutes...

Whatever you do, just don't do it while on stage.

@LightnessRacesinOrbit I think the point was not that it was a regular occurrence, but rather, given the context in the question, because you did something dumb and ate or drank something you probably shouldn't have eaten or drank in that quantity. Not the brightest idea in general, especially before going on stage for whatever reason, but also not a medical condition, just a temporary lack of self-control. :p

@neminem: Well either see a stomach doctor or someone who can help you with basic life organisation skills I suppose, yeah ;)

Just to go along with a posted answer, you could give a copy of your lecture notes to a TA prior to the lecture so they're prepared to teach any part that you're unable to cover. If you think you are so ill as to necessitate frequent breaks, though, consider staying home and maybe visit an acute care clinic.

Take a small break and I'll be back in 5 minutes - and you take off the microphone

Ideally, you use the bathroom before lecturing which should prevent you from needing the bathroom during the lecuture. In cases where you are unwell, I find it best to let the class know ahead of time to tell them you are unwell and might need to suddenly excuse yourself, but that you will be back.
Regardless of if you have told the students in advance, if you must excuse yourself, do it politely and tell them you will be back in a few moments.

I'm agreeing.  There's really nothing too specific about this compared to any other job.  If you're unable to do a job (regardless of how public your performance is), sometimes you just need to explain that you're excusing yourself, set any expectations that are required (like when you estimate that you'll be back), and then do whatever you have to do.  People understand bathroom needs, medical needs, etc.  It might be a less polished performance, and some people might be less forgiving of "imperfection" than others, but sometimes we imperfect people have to just do the best that we can.

for my own classes, I prepare with anticipation:
1) an exercise that students could complete while I am away from the Classroom or
2) show an instructional video and ask students to fill a questionnaire at the end to evaluate their comprehension of the presentation.
If there is no need to use these resources, then I just left them as assignment for next class.
Ideally, in our 21st century, every teacher should be able to record their own classes in video.  In case of an unexpected emergency, students watch this lesson's recording, at least in that day.

A plausible reason is if the instructor becomes ill, and this manifests partway through a lecture.
In this case, the only thing they can do is politely explain that they are unwell.
If a teaching assistant is on hand, they may be able to take over the lecture. If not, they may choose to invite the students to use the room and time remaining for self instruction. At the university level, students should, as a group, be able to fill in the blanks for a missed half lecture.
In either case, a follow up email indicating that the next class either will or will not precede as scheduled is probably a good idea. This may include information on a time, or times, when the professor will be available to provide clarification on the subjects that were unexpectedly omitted. It should probably not include the details of the illness, unless it is sufficiently serious as to merit inclusion to explain why the professor is changing mid-semester.


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The capacity to get research funding, how to explain my reply?
I am going to apply for a research position. There are several questions in the formula that I have to fill up. One is "The capacity to get research funding".  I do not understand what I have to write as an answer for this sentence. Is it enough to put the  previous fundings that I got? A couple of years ago, after my Phd I was awarded a research grant. Do I need to explain anything special about them? Or just list them. They asked this question along with some other questions under the title "Selection Criteria".
Thanks for your help and time.

What you want to do with your answer is to make the case that you will most likely get grants in the future, if you were to be hired.
That you have been successful with a grant application in the past tends to be the best factual basis for such a claim. However, your narrative should be forward-looking. Is the grant you got similar to those grants you'd be applying for in that position? If not, how will you adapt? Do you have other good ideas for grants? Are you aware of the relevant funding bodies?
I'd expect this question to be one of the most important ones, if not the most important one. The amount of detail you give compared to other questions should probably reflect that.

It is impossible to know how much detail they require unless you ask them. Assuming you have a history of successful funding, just ask how much detail they want beyond a list of past success.
A few words about the relevance of your research to potential funding organizations would probably be wise to add in any case.


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Acknowledgment part of manuscript before submission
I am going to submit a manuscript to a journal. Should the acknowledgment section be written after the acceptance of the article or it can be written in the first step of submission? In my case, I would like to express my appreciation to a professor that I had some useful discussion with him, in that part.

It probably doesn't matter as it is unlikely that it would be of concern to the reviewers. But there is no reason to withhold it either. Yes, it can be submitted in the first submission.
An exception might be if you were hiding the identity of a person who might possibly be a reviewer and the editor didn't know the connection, but for an advisor this isn't a likely scenario.

I've always included the acknowledgements section in the initial submission. For journals in my field, it is more or less required because certain disclosures like funding sources occur in that area. It's also a hint to the editor that the people acknowledged are likely too close to the work to serve as impartial peer reviewers.
For journal manuscripts, it would be unusual to me to acknowledge someone for anything besides contribution to the manuscript at hand that does not rise to the level of authorship. In contrast, in a thesis it's normal to include personal notes of appreciation (though this may vary by country/field). So, if your professor has contributed to this manuscript in some way, such as by providing advice or suggestions to the manuscript, it's appropriate to express your appreciation for those contributions and it's appropriate to do so in the initial submission.