The decision of fundamental problems of the origin and evolution of the solar system requires a comprehensive research of asteroids. The last decade is marked by numerous discoveries of satellites of asteroids. The investigation of these satellites gives: a) the possibility to determine masses, densities and other physical characteristics of asteroids with higher precision; b) some information for development of means of protection of the Earth from collision with an asteroid and also for planning and progression of flights to asteroids with the purposes of their scientific research and use of their natural resources for needs of mankind. We give the observational data on the known satellite systems. The methods for detection and investigation of their basic characteristics, probable mechanisms of formation of satellites of asteroids, and stability of their movement are described.