What is an overview of the main interpretations of "day" in Genesis 1? In the Creation account in Genesis 1 (and 2), God's work of Creation is famously split into 7 "days". For example, the first "day" occurs in verse 5:


  Genesis 1:5 (NLT)
  God called the light "day" and the darkness "night."  
  
  And evening passed and morning came, marking the first day.


I have seen claims that "day" refers to a literal 24-hour period, which is supported by the fact that the same Hebrew word is used for both occurrences of "day" in that verse. I have also seen claims that "day" just refers to some long period of time, which is in agreement with scientific evidence. Hence, my question is:

Considering context and wording, what are the main interpretations of "day" in Genesis 1?
There are three primary views that explain the meaning of the word "day" in Genesis 1. I will describe each one, and some of the purported Biblical evidence supporting each, briefly here. After all, this is a topic on which many books have been written.


24-hour Day Theory

This view, which is held by many Young Earth Creationists states that each of the 6 days were 24-hours long. Although they admit that the Sun was not created until the third day, this does not mean that the first two days could not have been 24-hours long, just the same.

A small sample of Biblical evidence to support this theory includes:


Genesis 1 mentions the passing of "morning" and "evening", this suggests literal days
A study of other Biblical texts which use the phrase "evening and morning" (38 not counting Genesis 1) all refer to 24-hour days
The Hebrew word for day (Yom) used in Genesis 1, whenever attached to a number elsewhere in scripture, it refers to a 24-hour day


See the book Creation and Time: A Report on the Progressive Creationist Book by Hugh Ross by Mark A Van Beber and Paul S. Taylor for more discussion on this, and relevant topics. Note: not to be confused with the book Creation and Time by Hugh Ross, to which the aforementioned book is a rebuttal.
1000-year Day Theory

Another view held by many Young Earth Creationists, it is essentially the same as the 24-hour Day Theory, with the exception that it acknowledges that God's perspective of time is different than the human perspective of time, in light of 2 Peter 3:8:


  But do not forget this one thing, dear friends: With the Lord a day is like a thousand years, and a thousand years are like a day.


Therefore, the Genesis 1 days may refer to 1000-year time periods, rather than 24-hour time periods.
Day-Age Theory

This view, a subset of Old Earth Creationism, is the view that the word "day" in Genesis 1 is metaphorical, and represents an arbitrary amount of time. Consistency with scientific evidence is frequently cited, but also often criticized by Young Earth Creationsts as taking too liberal a view of scripture.

A small sample of Biblical evidence to support this view includes:


The Hebrew word for day (Yom) used in Genesis 1 has many meanings: (a) Some portion of the daylight (hours), (b) Sunrise to sunset, (c) Sunset to sunset, (d) A segment of time without any reference to solar days (from weeks to a year to several years to an age or epoch) [i.e. "In my grandfather's day" or "in the day of the dinosaurs]
In rebuttal to point #2 above, the argument is made that none of these 38 mentions of "evening and morning" use the same Hebrew word for day (Yom), so drawing parallels is inappropriate
In rebuttal to point #3 above, the argument is made that when used elsewhere in the singular (as it is in Genesis 1) the Hebrew word (Yom) is always in reference to human activity, therefore drawing parallels to this usage in Genesis 1 in this case is also inappropriate
The fact that the seventh day never ended suggests that we are still living in the seventh day, which would clearly indicate that the seventh "day" is many years long.
The Genesis 2 re-account of creation has Adam naming "all the wild animals and all the birds" (Genesis 2:19-20 NIV) between his own creation and before Eve was created, thus all on the 6th day. This would be impossible in a 24-hour period (Young Earth creationists often argue that God may have given Adam supernatural speed or abilities, or that prior to the fall man naturally had greater abilities that might allow this task to be completed in one day.)


See the book A Matter of Days by Hugh Ross for additional discussion of these topics.