  We prove that any affine, resp. polarized projective, spherical variety
admits a flat degeneration to an affine, resp. polarized projective, toric
variety. Motivated by Mirror Symmetry, we give conditions for the limit toric
variety to be a Gorenstein Fano, and provide many examples. We also provide an
explanation for the limits as boundary points of the moduli space of stable
pairs whose existence is predicted by the Minimal Model Program.
