Spintronics of antiferromagnets is a new and rapidly developing field of the physics of magnetism. Even without macroscopic magnetization, antiferromagnets, similar to ferromagnetic materials are affected by spin-polarized current, and as in ferromagnets this phenomenon is based on a spin-dependent interaction between localized and free electrons. However, due to the nature of antiferromagnetic materials (complex magnetic structure, essential role of exchange interactions, absence of macroscopic magnetization) the study of possible spintronic effects requires new theoretical and experimental approaches. The purpose of this review is to systemize and describe recent developments in this area. After presenting the main features of structure and behavior of antiferromagnets various microscopic and phenomenological models for description of the current-induced phenomena in heterostructures containing ferro- and antiferromagnetic layers are considered. The questions related to an effect of antiferromagnetic ordering on an electric current, as well as the questions of possible creation of fully antiferromagnetic spin valves are discussed. In addition, we briefly discuss available experimental results and try to interpret them.