The very special characteristic of the proximity effect in superconductor-ferromagnet systems is the damped oscillatory behavior of the Cooper pair wave function in a ferromagnet. In some sense, this is analogous to the inhomogeneous superconductivity, predicted long time ago by Larkin and Ovchinnikov (1964), and Fulde and Ferrell (1964), and constantly searched since that. After the qualitative analysis of the peculiarities of the proximity effect in the presence of the exchange field, the author provides a unified description of the properties of the superconductor-ferromagnet heterostructures. Special attention is paid to the striking non-monotonous dependance of the critical temperature of the multilayers and bilayers on the ferromagnetic layer thickness and conditions of the realization of the "Pi"- Josephson junctions. The recent progress in the preparation of the high quality hybrid systems permitted to observe on experiments many interesting effects, which are also discussed in the article. Finally, the author analyzes the phenomenon of the domain-wall superconductivity and the influence of superconductivity on the magnetic structure in superconductor-ferromagnet bilayers.