Good Survey paper for k-means/k-median/k-center/facility-location I have stated 4 problems in the Question title.
All these problems are closely related and are studied in various variations. For example:

Space: Euclidean/metric/discrete/continuous/non-metric/2-D_plane...

Parameters: when $k$ or $d$ is fixed or some sort of bi-critera relaxation ...

Settings: Streaming/Online/parallel/Fault-tolerant/query/...

Constrained models: capacitated/outlier/fairness-constraints/...

Special models: $\beta$-separation/ORSS-separability/BBG-condition/...

Techniques: coreset-based/primal-dual/local-search/distance-sampling/tree-decomposition/...

...many more


There are several hardness results, approximation algorithm and parameterized algorithms known for the problem and its variants; and many are not known yet and are open.
Sometimes it happens that the research papers mention imprecise/incomplete/incorrect results, that have been previously discovered. This causes a lot of confusion. Moreover, it is difficult to go through every paper and check their results. I am looking for a (survey) paper that might give a brief idea of what all has been done in the field over the years and what are the open questions remaining in the field. It would be a great help if somebody could share such a paper.
Recently, I came across the following survey: Recent Developments in Approximation Algorithms for Facility Location and Clustering Problems
The authors only discuss the major results and mention some interesting open problems at the end.