Overwhelming observational evidence suggests that 85% of all the matter in the universe is dark matter, a particle whose microscopic properties remain poorly constrained over many orders of magnitude. The current, widely assumed standard paradigm of a collisionless, cold dark matter (CDM) and dark energy cosmology called ΛCDM has proven to be very successful on large scales. Yet, observed galaxies are generally less dense than simple CDM-only predictions, and while CDM is often assumed to be a single, collisionless particle species, there are no Standard Model particles that are similarly collisionless. In this talk, I will briefly discuss three possible models which give rise to dark matter self-interactions and a subset of their astrophysical implications and constraints: 1) self-interacting dark matter (SIDM), in which dark matter interacts only with itself non-gravitationally through 2-2 scattering events, 2) dark-U(1) charged dark matter which couples only to itself non-gravitationally via long-range interactions, and 3) milli-charged dark matter (mDM), in which dark matter couples electromagnetically with itself and with the Standard Model. I will start by discussing hydrodynamic simulations demonstrating SIDM-induced delay of super-massive black hole growth in Milky-Way mass galaxies. I will then present semi-analytic calculations that show streaming mDM and dark-U(1) dark matter can cause transverse electromagnetic Weibel plasma instabilities in galactic systems, such as in merging galaxies clusters. Finally, I will demonstrate how these instabilities lead to significant constraints on the mDM and dark-U(1) dark matter parameter space.