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Nonlinear optical phenomena are widely used for the study of semiconductormaterials. The paper presents an overview of experimental and theoreticalstudies of excitons by the method of optical second and third harmonicsgeneration in various bulk semiconductors (GaAs, CdTe, ZnSe, ZnO, Cu$_2$O,(Cd,Mn)Te, EuTe, EuSe), and low-dimensional heterostructures ZnSe/BeTe.Particular attention is paid to the role of external electric and magneticfields that modify the exciton states and induce new mechanisms of opticalharmonics generation. Microscopic mechanisms of harmonics generation based onthe Stark effect, the spin and orbital Zeeman effects, and on the magneto-Starkeffect specific for excitons moving in an external magnetic field areconsidered. This approach makes it possible to study the properties of excitonsand to obtain new information on their energy and spin structure that is notavailable when the excitons are investigated by linear optical spectroscopy. Asa result of these studies, a large amount of information was obtained, whichallows us to conclude on the establishing of a new field of research - excitonspectroscopy by the method of optical harmonics generation.

Exciton spectroscopy of semiconductors by the method of optical harmonics generation