Given a smooth Fano variety, Mirror Symmetry predicts the existence of a so called Landau--Ginzburg model --- a pencil, whose symplectic geometry reflects the algebraic geometry of the Fano variety, and viceversa. We discuss this relation for mirror symmetry conjecture of Hodge structure variations that translates this relation to a quantitative level. We discuss (mostly for threefolds) how, given Landau--Ginzburg model, predict some numerical invariants of Fano variety (Gromov--Witten invariants, Hodge numbers, characteristic numbers) and its birational type. We also discuss the relations of particular weak Landau--Ginzburg models with toric degenerations.