A review is given of investigations of pulsed high-pressure volume discharges excited by fast-electron beams. The following topics are discussed: classification of discharges; methods for calculating the current-voltage characteristics; analysis of the optimal ways of depositing energy in the gas in the volume stage of the discharge; discharge instability mechanisms and the corresponding experimental observations; applications of discharges. The results are given of calculations of the electric field in the cathode and anode regions, and also in the discharge column in the case of a spatially inhomogeneous ionication of the gap. It is shown that a stable volume flow of the current in molecular gases in which the specific deposited energy is 0.1--1 J/cm$^3$ may be attained in a nonself-sustaining discharge and in a discharge with ionization multiplication. In both cases a spark channel appears in two stages: formation of sparkinitiating centers in the form of plasma regions with a higher density near the electrodes is followed by growth of the spark channel from such initiating centers. In some cases the spark channel growth can be described by the available mathematical models. Discharges in mixtures of rare gases with halogencontaining compounds, when electrons are lost mainly by capture by complex molecules, are considered separately. Applications of volume discharges in laser pumping, switching of pulsed currents, plasma chemistry, etc., are described.