MV (Mirkovic-Vilonen) polytopes control the combinatorics of a diverse array of constructions related to the representation theory of semi-simple Lie algebras. They arise as the moment map images of MV cycles in the affine Grassmannian. They describe the combinatorics of the PBW construction of the canonical basis. And they control the submodule behavior of modules for preprojective algebras and KLR algebras. Recently, there has been much work toward extending this picture to the case of affine Lie algebras. I will give a brief overview of the current state of affairs, focusing on some rank-2 results (joint with P. Tingley) and some type A results on MV cycles.