  Mirkovi\'c-Vilonen (MV) polytopes are a class of generalized permutahedra
originating from geometric representation theory. In this paper we study MV
polytopes coming from matroid polytopes, flag matroid polytopes, Bruhat
interval polytopes, and Schubitopes. We give classifications and combinatorial
conditions for when these polytopes are MV polytopes. We also describe how the
crystal structure on MV polytopes manifests combinatorially in these
situations. As a special case, we show that the Newton polytopes of Schubert
polynomials and key polynomials are MV polytopes.
