The review deals with new results in the theory of electron localization in disordered systems and with experiments which have been stimulated by these results. An elementary scaling theory of localization and its consequences are discussed. Attention is concentrated on the phenomenon of localization in two-dimensional systems. The main experiments on the conductivity of thin metal wires and films, demonstrating qualitatively new behavior associated with localization, are discussed. The review concludes with a brief look at the problems of deriving a self-consistent scaling theory of critical behavior at a mobility edge.