Homological mirror symmetry is a relation between algebraic and symplectic sides of geometric objects. Originally mirror symmetry came from physics, but the homological mirror symmetry conjecture, formulated by M. Kontsevich for Calabi-Yau varieties, is an attempt to give a mathematical explanation of this phenomenon. We will try to describe the main principles of homological mirror symmetry and its extention to the non-Calabi-Yau case. We will explain how Landau-Ginzburg models appear in mirror symmetry, and will give some examples of mirror symmetry where noncommutative deforamations of varieties are directly related to variation of the symplectic form in LG-models.