In this review, the theory of low energy electron scattering by light atoms and ions is first presented. The theory is then extended to treat electron scattering by heavy atoms and ions where relativistic effects are important. Electron scattering by atoms and ions at intermediate and high energies, and the threshold behavior of the ionization cross section are then reviewed. Finally the theory of scattering of electrons by molecules is discussed, where the possibility of exciting degrees of freedom associated with the nuclear motion is considered. In all of these areas, computer program packages which enable accurate scattering data to be calculated are referenced. ©2000 American Institute of Physics.