From this brief review, one can see that the study of the local Universe - our Galaxy, its near neighbours, and nearby galaxies in general - provides many contraints on the dark matter problem, including on what it actually may consist of. The study of the more distant Universe is complementary to this, and though the next generation of large telescopes should provide a lot more information on it, only a combined approach will solve the entire dark matter problem.
I would like to thank Lia Athanassoula for her comments on the manuscript while it was being written, and for frequent discussions of the dark matter problem in general.