Runaway electrons (RAEs) generation in high-pressure gases is an important physical phenomenon that influences significantly discharge shapes and properties of initiated plasma. The diffuse discharges formed due to RAEs in air and other gases at atmospheric pressure find wide application. In the present review, theoretical and experimental results that explain the reason for the RAEs occurrence at high pressures are analyzed and recommendations are given on the implementation of conditions under which the runaway electron beam (RAEB) with the highest current can be obtained at atmospheric pressure. Experimental results were obtained using subnanosecond, nanosecond, and submicrosecond generators, including those specially developed for runaway electron generation. The RAEB were recorded by oscilloscopes and collectors with picosecond time resolution. To describe theoretically the phenomenon of continuous electron acceleration, the method of physical kinetics has been used based on the Boltzmann kinetic equation that takes into account the minimum but sufficient number of elementary processes, including shock gas ionization and elastic electron scattering. Results of modeling allowed the main factors to be established that control the RAE appearance, the most important of which is electron scattering on neutral atoms and/or molecules. Theoretical modeling has allowed the influence of various parameters (including the voltage, pressure, gas type, and geometrical characteristics of the discharge gap) to be taken into account. The results of research presented here allow the RAEs accelerators with desirable parameters to be developed and the possibility of obtaining diffuse discharges to be accessed under various conditions. The review consists of the Introduction, 5 Sections, the Conclusion, and the References.