A matroid polytope (or matroid basis polytope) is the convex hull of the indicator vectors of the bases of a matroid. Matroid polytopes have found charming application in a number of more explicitly combinatorial contexts. Recently they reappeared in a proof by Ardila, Rincon, and Williams on the positive Grassmannian and its oriented matroid analog. In a future talk I plan to discuss this new proof. The present talk will be a general introduction to matroid polytopes, stressing elements relevant to the ARW proof.