A review is given of theoretical and experimental papers on the injection of high-current relativistic electron beams into plasma and neutral gas. The review begins with work on the equilibrium configurations of electron beams which are partially or completely neutralized in current and charge; limiting beam currents which can be achieved in different equilibrium configurations are determined. The establishment of equilibrium during the injection of relativistic electron beams into plasma and neutral gas is discussed next. In the case of injection into plasma, particular attention is paid to the neutralization of charge and current, whilst in the case of injection into neutral gas the ionization of the latter and the capture and acceleration of the resulting ions in the space-charge field on the leading front of the beam are also discussed. The results of experimental studies are given and are compared with existing theoretical descriptions.