There is now overwhelming evidence that more than eighty percent of the mass in the Universe is dark matter. This provides a clear indication for the existence of a particle or particles beyond the standard model, but we have yet to determine the nature of this particle. Models of dark matter make specific predictions for the formation of cosmological structure on a wide range of scales, from the shapes of and substructures within galaxies to the distribution of matter over cosmological distances. I will outline how theoretical predictions, simulations, and observations of cosmological structure formation shed light on the distribution and particle nature of dark matter. This includes both how they inform our understanding and interpretation of limits and signals from dark matter, direct and indirect detection experiments, and how astrophysical measurements can complement these studies.