The review covers theoretical and experimental studies of the parametric effect of high-power electromagnetic radiation on a plasma. Under the action of such a field, parametric instabilities develop in a plasma, leading to appearance of a turbulent state with an increased level of fluctuations of the internal field in the plasma. Under the action of these fluctuations the particle distribution in the plasma changes and, in particular, their energy increases, which corresponds to anomalously fast transfer of the energy of the radiation field to the plasma particles or, in other words, corresponds to an anomalous increase of the high-frequency conductivity of a parametric ally unstable plasma. This theoretically predicted pattern find confirmation in a number of experimental investigations, also discussed in the review. Experiments demonstrate the appearance, under the action of high-power radiation, of an increased level of plasma fluctuations, a large high-frequency resistance, an increase in the rate of plasma heating, and, finally, of fast particles. All of these effects are consistent with the theoretical ideas and permit us to discuss qualitatively a new group of physical phenomena arising in the action of high-power radiation on a plasma.