Let Gr(k,n) be the Grassmannian of k-planes in C^n. The standard torus action on C^n induces a torus action on Gr(k,n), whose orbits encode interesting combinatorial and geometric invariants. I will discuss explicit degenerations of the generic torus orbit closure into a union of Richardson varieties, and a further degeneration in the union of Schubert varieties. These give new proofs of cohomological formulas of Berget-Fink and Klyachko, respectively. I will speculate about where to go from here.