A review is given of both theoretical and experimental investigations of the sputtering as a result of strong excitation of the electron subsystem of a solid by fast and multiply charged ions. A systematic account is given of the main experimentally established relationships governing inelastic sputtering. An analysis is made of the dependences of the inelastic sputtering coefficient on the energy and charge of the incident ions and on the target structure, and of the differential characteristics of the sputtered particles. Theoretical investigations of the electron-excitation region and its relaxation, of the transfer of the electron energy to the target atoms, and of the inelastic sputtering models are discussed. A brief account is given of the history of the topic, of possible practical applications of inelastic sputtering, and of its relationship to other phenomena.