Understanding the fundamental nature of dark matter is one of the major challenges facing the physics community today. Direct and indirect detection efforts search for dark matter interactions with the Standard Model of particle physics, but no concrete evidence has been observed. In this talk, I will discuss how cosmological observables can be used as complementary probes of dark matter physics. In particular, I will describe the effects of dark matter scattering with protons and electrons in the early Universe and show constraints using CMB anisotropies and the Milky Way satellite abundance.