This review presents systematically the results of investigations of the physics of high-current discharges in dense low-temperature plasmas and it is based, to a considerable extent, on the results of theoretical and experimental investigations carried out since 1967 at the Lebedev Physics Institute and in the Physics Department of the Moscow State University. The prime aim of these investigations was to determine the possibility of using high-current discharges in dense plasmas as radiation sources for the pumping of modern high-power lasers. It was found that the physics of high-current light-emitting discharges went well beyond the utilitarian task of providing high-power light sources, and covered little known branches of the physics of dense plasmas at relatively low temperatures, when the radiation dominated the energy balance and transfer processes. This general approach to the physics of plasmas is adopted in the present review. It comprises a theoretical part (Chap. I), which deals with the results of theoretical analyses of the formation, equilibrium, and stability of plasmas in high-current light-emitting discharges, and a part (Chap. II) which gives the results of an experimental investigation of the physical processes in such discharges and analyzes their characteristics as light sources. The review is intended for physicists and engineers investigating high-power light sources, magnetohydrodynamics, and physics of dense low-temperature plasmas. The review covers papers which appeared up to the beginning of 1973.