The status of research on glow discharges in a gas flow, used in pumping fast-flow lasers, is reviewed. Systematic study of this discharge began about 10 years ago. This discharge form, according to a number of properties (current flow mechanism, nature of the development of instabilities, etc.), differs considerably from the well-studied glow discharge in tubes. One of the distinguishing features of such a discharge is the negligibly small role of ionization in a large part of the positive column, so that narrow regions near the electrodes contribute most of the positive ions and electrons. Negative ions, which compensate the charge of the positive column, are generated in its volume. The discharge turns out to be weakly inhomogeneous in the direction from the cathode to the anode and the ion currents can form an appreciable part of the total current. These facts have not yet been sufficiently widely discussed in reviews and monographs. In this review, results of experimental investigations of the mechanism of current flow, energy balance, plasmochemical processes, and discharge instabilities are presented, the mathematical models used in their analysis are analyzed, and the possibilities for increasing the stability and efficiency of the discharge in fast-flow lasers are examined.