Abstract：Mirror Symmetry relates a Fano variety to its dual object --- Landau--Ginzburg model. Such models are one-dimensional Calabi--Yau varieties that are dual to anticanonical sections of Fano varieties. The most studied higher-dimensional case of smooth Fano varieties is the threefold one: due to Iskovskikh and Mori--Mukai they are classified, and their geometry is well studied. On the other hand Landau--Ginzburg models for them are constructed. We shortly observe the construction.

We also discuss properties of Landau--Ginzburg models that reflect the geometry of their corresponding Fano varieties: rationality, Hodge numbers, etc., and algebro-geometric conjectures on Fano varieties based on them. Finally, we discuss derived categories of Fano varieties, their relations to Landau--Ginzburg models,and some recent predictions based on the observations.