Abstract: Classical and quantum scattering theory studies how the nature of the potential energy of a mechanical system affects its longtime dynamics. I will survey some aspects of this vast theory, emphasizing the method of Enss, which has a “geometric” (as opposed to functional-analytic) flavor. Then, I will describe work with Tal Malinovitch on quantum scattering in Euclidean space off of potentials satisfying certain geometric conditions on their support. The potentials we consider are anisotropic in that they decay at infinity, but only within a collection of cones. For such potentials, we obtain microlocal descriptions of the scattering states, which behave like free waves as time goes to infinity, as well their complement, which consists of states that interact with the potential at long time scales.