The review is devoted to the research and applications of nonlinear and linear adaptive optics to improve the quality of high power laser beams, including the conditions of its propagation in optically inhomogeneous media. The application of nonlinear adaptive optics is associated with the phase conjugation (wavefront reversal) at stimulated Brillouin scattering in focused beams. The problems of obtaining the high-quality wavefront self-reversal and achieving the diffraction-limited radiation divergence are considered using the example of a two-pass explosive photodissociation iodine laser created at the dawn of quantum electronics and largely determined the energy horizons of its evolution. Linear adaptive optics is associated with an active effect on the radiation phase using methods based both on phase determination and on optimization algorithms. In the case of multichannel lasers, the problem of coherent beam combination is considered, and in the case of a single-channel laser, wavefront control using deformable mirrors is considered. Features of adaptive phase control in the case of continuous and pulsed radiation are discussed.