I work with the Fano varieties and their properties prescribed by the Mirror Symmetry. In particular I do the degeneration of Fano varieties to toric ones and try to describe Fano varieties by their quantum D-module (Gromov-Witten invariants). For these I use (and sometimes justify) things like recently constructed hidden integral structures in the quantum cohomology, homological mirror symmetry and arithmetic of Landau-Ginzburg models mirror dual to Fano varieties.