Galaxy clusters are the largest virialized structures in the universe, containing thousands of galaxies and spanning of order 1 megaparsec across. Only about 3% of their mass is actually in galaxies, with about 15% of their mass in diffuse gas that has been stripped from the galaxies, and the remainder in dark matter (DM).  When two clusters collide, the three components (galaxies, gas, DM) show interestingly different behaviors that reveal their collisional or noncollisional nature. We can use this to constrain the extent to which (if at all) DM particles scatter off each other. This astrophysical argument complements constraints, from collider and other experiments, on interactions between dark matter particles and standard model particles.  Constraints on DM-DM interactions can only be obtained astrophysically, and as time permits I will touch on other astrophysical arguments that constrain DM-DM interactions.