The article discusses the history of the discovery of intense bursts of cosmic gamma rays in the Vela group of satellites. A summary is given of the data on observation of gamma-ray bursts in various space instruments. The possibilities of terrestrial observation of phenomena due to the gamma bursts are discussed. Various models of the gamma bursts are analyzed: stellar flares, the activity of neutron stars, nonstationary accretion into compact objects, explosions of supernovae, and the collapse of supermassive bodies in the nuclei of active galaxies. The prospects for futher study of cosmic gamma-ray bursts are discussed.