This review covers the current theoretical concepts and experimental methods employed in studying the two-dimensional electron density of states in a magnetic field. The authors discuss the different factors that determine the energy distribution of the density of states in real systems. They demonstrate the importance of the screening of random external potential fluctuations by two-dimensional electrons and particularly the oscillatory dependence of screening on electron concentration. When considering the various theoretical approaches and experimental methods, the authors analyze their conditions of applicability and the self-consistency of obtained results. They demonstrate that it is possible to evaluate experimentally the random potential amplitude and range from the oscillations in Landau level broadening.