A detailed review is given of modern theoretical ideas on the absorption of powerful laser radiation by plasmas. The linear theory of collisional absorption and linear wave conversion are examined, as are the results of the nonlinear theory of inverse bremsstrahlung. The results of theoretical analyses of the nonlinear interaction between radiation and moving plasmas are presented. The unusual qualitative features of the nonlinear electrodynamics of moving media that appear when the flow velocity is comparable with the velocity of sound are demonstrated. The phenomenon of field self-limitation in ultrasonic plasma flows is described. The fundamentals of the theory of parametric absorption and of the theory of absorption by plasma with well developed ion-acoustic turbulence are presented.