I will present a `wish list' of open problems in toric geometry arising from heterotic string theory. Specifically, I will discuss CY 3-folds, X, defined as hypersurfaces in toric 4-folds (via Batyrev's reflexive polytope construction) and problems in determining the Kahler and Mori cones of X. I will also cover discrete automorphisms of X and tools for analyzing stable vector bundles over torically realized CYs.