The present state of research on the resonant scattering of electrons by atoms and ions is described. A comparison is made of the various theoretical methods used to describe these processes: the method of strong coupling of channels, the diagonalization method, the R-matrix method, etc. For the most part, the latest experimental data over the past five years (through the end of 1984) are reported. Only isolated references are made to 1985 studies. The thrust of the review is to determine the role played by autoionizing states in resonant scattering and to analyze how well the existing theoretical studies describe the experimental data available. It can be concluded from this analysis that we have a fairly clear picture of the mechanism for resonant scattering processes and that the description is qualitatively good. However, an important role is played here by electron-electron correlations. Further research is required for an accurate account of these correlations.