Membrane gas separation using polymeric membranes is one of rapidly developing energy-conserving technologies. This review describes the scope of membrane gas separation problems and demonstrates the relevance of membrane methods for their solution. The basic concepts and regularities of diffusion gas transfer and principles and characteristics of membrane gas separation are considered. The main physicochemical approaches to the selection of membrane materials considering both the properties of the gas–polymer system and the structure and physical properties of polymers are discussed. The considered issues are combined within a common approach to substantiate the choice of both existing commercial polymers and advanced polymeric materials to address important gas separation problems such as separation of air components; carbon dioxide, hydrogen and helium recovery from natural and industrial gas mixtures; and separation of a nitrogen and methane mixture. The avenues of development of the membrane materials science to solve each of the mentioned problems of membrane gas separation are demonstrated. The review is intended for specialists in the synthesis and physics of polymers for planning the research and assessing the applicability of polymeric materials for various practical gas separation problems and for specialists in the membrane materials science and membrane technology. <br> The bibliography includes 165 references.