A review of experimental and theoretical research on the Faraday effect in a new class of materials–semimagnetic semiconductors (SMS). The authors discuss the mechanism responsible for the giant Faraday effect in SMS, which is based on s, p–d exchange interactions of excitons, electrons, and holes with magnetic ions. The authors also examine the dependence of Faraday rotation (FR) on wavelength, magnetic component concentration, temperature, and magnetic field intensity in A$^2$B$^6\langle$Mn$\rangle$ and A$^2_{1-x}$Mn$_x$B$^6$ crystals, as well as other SMS (GaAs $\langle$Mn$\rangle$, CdP$_2\langle$Mn$\rangle$, Pb$_{1–x}$Mn$_x$I$_2$). They examine the use of FR in the study of the paramagnetic-spin glass transition, the role played by relaxation processes involving magnetic Mn$^{2+}$ ions, excitons, and polarons in the direct and inverse Faraday effects, and the properties of FR in thin SMS films and spin superlattices. Finally, the authors analyze possible applications of the Faraday effect in SMS to practical magnetooptic devices (optical isolators, fiber optic magnetic field sensors).