The familiar (to this audience) geometric Satake correspondence can be used to shed light on recent work of several authors concerning the equivariant and quantum cohomology of the Grassmannian. In this talk, I will show how some well-known formulas in Schubert calculus can be deduced from geometric Satake, suggesting extensions to other minuscule $G/P$ and beyond. This point of view was inspired by work of Golyshev and Manivel, and is part of joint work with Antonio Nigro.