The conditions for the formation of close binaries containing main-sequence stars, degenerate dwarfs of various types, neutron stars, and black holes of various masses are considered. The paper investigates the evolution of the closest binary systems under the influence of their gravitational-wave radiation. The conditions under which the binary components can merge on a time scale shorter than the Hubble time as a result of their emission of gravitational waves are estimated. A self-consistent scenario model is used to estimate the frequency of such events in the Galaxy, their observable manifestations, the nature of the merger products, and the role of these events in the evolution of stars and galaxies. The conditions for the formation and evolution of supermassive binary black holes during collisions andmergers of galaxies in their dense clusters are studied.