A review is given of theoretical descriptions of the nonlinear interaction of negative ions with a strong optical field. A brief account is provided of the main features of the structure of negative ions. A detailed analysis is made of the theoretical methods for describing nonlinear processes in negative ions on the basis of the one-electron approximation. The ranges of validity of the reviewed methods are given. Special attention is paid to the role of the electron-electron correlation interaction. The importance of the correlation interaction in weakly nonlinear processes is stressed. The review concludes with the formulation of a number of theoretical and experimental tasks for future investigations of nonlinear processes in negative ions.