The affine Grassmannian is a very important object in geometric representation theory, and its central degeneration shows up in Gaitsgory's central sheaves and local models of Shimura varieties. In this talk, I will explain the central degeneration of semi-infinite orbits, Mirkovic-Vilonen cycles and Iwahori orbits in the affine Grassmannian. I will also use convex polytopes to illustrate some interesting examples.