The hypothesis of Cold Dark Matter (CDM) has been spectacularly confirmed on the largest scales of the Universe and must now be stress-tested on sub-galactic scales.   Many well-motivated and generic alternatives to CDM can leave spectacular signatures on precisely these scales, affecting the evolution of galaxies as well as their population statistics.  Excitingly, over the course of the next decade, a flood of astrophysical data will open the possibility of searching for these distinctive imprints and shedding light on key questions about dark matter.  In interpreting such results, systematic studies using both semi-analytic codes and numerical simulations will play a critical role in robustly disambiguating dark matter signals from other standard baryonic processes.  As a concrete example, I will describe the consequences for galaxy formation when the dark matter can self-scatter, highlighting the scenario where the interactions are dissipative and a sub-component of the dark matter efficiently cools inside galaxies.