This article reviews the most recent experimental approaches to the study of, and the results of investigations of multi-electron secondary emission resulting from the bombardment of the surface of a solid by atomic particles with energies of 1--10$^3$ keV. The results of measurements of the differential characteristics of secondary electron emission (emission statistics, energy and angular distributions) are discussed. Theoretical approaches to a quantitative description of the principal characteristics of multi-electron secondary emission are considered, and the results of a Monte Carlo modeling, reproducing the principal observed MUSE effects are discussed.