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The most fundamental example of mirror symmetry compares the Fermathypersurfaces in P^n and P^n/G, where G is a finite group that acts on P^n andpreserves the Fermat hypersurface. We generalise this to hypersurfaces inGrassmannians, where the picture is richer and more complex. There is a finitegroup G that acts on the Grassmannian Gr(n,r) and preserves an appropriateCalabi-Yau hypersurface. We establish how mirror symmetry, toric degenerations,blow-ups and variation of GIT relate the Calabi-Yau hypersurfaces insideGr(n,r) and Gr(n,r)/G. This allows us to describe a compactification of theEguchi-Hori-Xiong mirror to the Grassmannian, inside a blow-up of the quotientof the Grassmannian by G.

Unwinding toric degenerations and mirror symmetry for Grassmannians