We review the present status of the experimental and theoretical research on the proximity effect in heterostructures composed of superconducting (S) and ferromagnetic (F) thin films. First, we discuss traditional effects originating from the oscillatory behavior of the superconducting pair wave function in the F-layer. Then, we concentrate on recent theoretical predictions for S/F layer systems. These are a) generation of odd triplet superconductivity in the F-layer and b) ferromagnetism induced in the S-layer below the superconducting transition temperature Tc (inverse proximity effect). The second part of the review is devoted to discussion of experiments relevant to the theoretical predictions. In particular, we present results of measurements of the critical temperature Tc as a function of the thickness of F-layers and we review experiments indicating the existence of the odd triplet superconductivity, cryptoferromagnetism and inverse proximity effect.