An account is given of the principal results of the theoretical and experimental investigations of the paramagnetic resonance absorption due to conduction electrons in metals. The physical principles of the phenomenon and the features which distinguish it from electron paramagnetic resonance in insulators are considered, and modern data on the resonance line shape and on the g factor are given briefly. A considerable part of the review is devoted to an account of the different mechanisms of spin relaxation of electrons in metals. In particular, a detailed survey is given of the results of recently performed theoretical and experimental studies of the problem of impurity relaxation in solid and liquid metals. In the final part of the article, the data available in the literature on the influence of surface effects on the spin resonance absorption are critically analyzed (these data are partly contradictory), and the question of the possibility of observing spin resonance in superconductors is briefly considered.