Abstract
The nature of dark matter is one of the most pressing questions in physics. Yet all our present knowledge of the dark sector to date comes from its gravitational interactions with astrophysical systems. Moreover, astronomical results still have immense potential to constrain the particle properties of dark matter in the near future. We introduce a simple 2D parameter space which classifies models in terms of a particle physics interaction strength and a characteristic astrophysical scale on which new physics appears, in order to facilitate communication between the fields of particle physics and astronomy. We survey the known astrophysical anomalies that are suggestive of non-trivial dark matter particle physics, and present a theoretical and observational program for future astrophysical measurements that will shed light on the nature of dark matter.