The present state of gamma-ray astronomy is reviewed. The basic understanding of the processes by which gamma radiation is generated and absorbed is outlined. The basic observational results in various gamma-ray energy ranges are presented. The nature of the gamma bursts, the radiation source at the center of the local galaxy, etc., are discussed for the range of soft gamma-ray energies (below a few tens of megaelectron volts), where radiation in gamma lines is predominant. In the very high-energy range ($E_\gamma\ge10^{12}$ eV) and in the ultrahigh-energy range ($E_\gamma\ge10^{15}$ eV) of the gamma radiation, the discussion focuses on discrete sources, in particular, the enigmatic source Cygnus X-3. Most of the review is devoted to an analysis of the origin of cosmic rays on the basis of the existing gamma-ray data over the energy range from a few tens of megaelectron volts to several gigaelectron volts. The question of determining the cosmic-ray gradient from gamma-ray data, the generation of high-latitude gamma radiation, the problem of the gamma-ray halo of the local galaxy, etc., are discussed. Also discussed are some theoretical models which explain the nature of the unidentified gamma-ray sources. Theoretical predictions and the results of measurements of the flux of gamma radiation from the supernova SN1987A are discussed.