Many of the oxides and chalcogenides formed by the 3d transition metals and 4f rare-earth metals are antiferro-, ferri-and ferromagnetic semiconductors. In this review, several theoretical aspects of these materials are discussed, including electron correlation in narrow bands and the formation of electrostatic and magnetic polarons. The problems of crystal growth and physical measurement are briefly considered, together with recent studies on the conduction mechanism in typical compounds like NiO, MnO, ferrites, garnets, CdCr2Se4and EuS. Finally, we comment on possible applications.