The present state of research on the cooling of atomic ensembles by means of laser radiation pressure is discussed. First the basic theory of resonance radiation pressure is reviewed. The effect of recoil on the drift and fluctuations of the momentum of an atom interacting with resonance radiation is examined. There is an analysis of the forces acting on an atom in some simple light fields: a traveling plane wave, a Gaussian beam, and counterpropagating Gaussian beams. The review then focuses on the monochromatization of atoms by resonance radiation pressure and related methods for laser cooling of atoms. The roles played by the radiation pressure force and by momentum diffusion in shaping the narrow velocity distributions of the ensemble of atoms are analyzed. The lowest temperature obtainable in the radiation cooling of atoms is estimated. The basic experimental methods for laser cooling of atomic beams are described. Problems of the three-dimensional cooling of atomic ensembles and problems of localizing cold atoms in light fields, steady-state magnetic fields, and electrostatic fields are discussed. The review concludes with a discussion of some applications of cold atoms in high-precision spectroscopy, frequency standards, and atomic physics.