The paper is a review of gas lasers pumped by runaway electrons preionized diffuse discharge (REP DD). The various conditions under which the discharge occurs are described. It is shown that in the presence of the highly non-uniform electric field strength distribution in a gap filled with dense gases, a stable diffuse discharge is ignited without the use of additional sources of ionizing radiation. This, in turn, is achieved by using discharge gaps, in which at least one of the electrodes has a small radius of curvature (e.g., “point-plane”, “blade-blade” and so on), and high-voltage (10s–100s kV) pulses with a (sub)nanosecond rise time. With this method of forming the discharge the runaway electrons can produce X-ray quanta in the gap and, together with them, provide preionization of the laser gas mixture. The dense nonequilibrium low-temperature plasma of this discharge can remain diffuse during the entire excitation time, including single pulse excitation and repetitive mode at the voltage pulse repetition rate up to several kHz. The properties and parameters of REP DD plasma are considered. Experimental and simulated characteristics of stimulated emission of REP DD plasma in various gaseous media are presented.