Evolution of close binary stars: theory and observations

We review modern concepts in the physics and evolution of close binary stars. The review is based, on the one hand, on numerical simulations of the evolution of their components and the processes that accompany that evolution and, on the other hand, on the entire set of observational information in all ranges of electromagnetic and gravitation-wave radiation. These concepts underlie modern astrophysics, the most extensive laboratory wherein the properties of matter in the Universe and the Universe itself are explored. We present the modern picture of the evolution of close binary stars, constructing which has been driving progress in the physics and evolution of astronomical objects for the last 50 years.