Soviet research on the propagation of intense relativistic electron beams (IREB) through fairly high-pressure air (pressure range 0.1 to 760 Torr) since the early 1970s has included the study of the plasma channel created by the passage of the electron beam through air, the resistive hose instability and its effect on beam propagation, the effect of self-fields, current enhancement, gas expansion, return currents, inherent beam energy spread, and other factors. This report covers Soviet developments in IREB propagation through air where the beam is not focused by external magnetic fields. The information was obtained from Soviet open-source publications with emphasis given to the last ten years of beam propagation in the Soviet Union. The volume of papers published on this subject in recent years indicates a significant increase in Soviet research in this area.