A review is given of the current status of research on photoelectromagnetic effects. A detailed analysis is made of the results of the more recent experimental studies of the anisotropy of the even and odd photoelectromagnetic effects, the effect across $p$--$n$ junctions, the effect at low temperatures (when the electron system is heated by the incident radiation and the electron temperature is higher than the lattice temperature), and the radiation electromagnetic effect (when a sample in a magnetic field is not illuminated but irradiated with a flux of ionizing particles). The experimental data are compared with the theory. Directions of future studies of the photoelectromagnetic effect are suggested.