This article reviews the present status of research on strongly nonequilibrium physical effects produced near and at the surfaces of metals, semiconductors, and dielectrics by high-power pulsed laser radiation, and their diagnostics by nonlinear-optical methods. The basic stages of the absorption and relaxation of the energy of laser radiation in the electronic and phonon subsystems of semiconductors and heating of the lattice are studied. The questions associated with fast laser-induced phase transformations in surface layers are discussed: melting-solidification and amorphous-solid-to-crystal and vice versa phase transitions, occurring with nano- and picosecond laser pulse durations (laser annealing). Different methods of laser diagnostics of the surfaces and nonequilibrium ultrafast processes on the surfaces of metals and semiconductors are reviewed. Special attention is devoted to nonlinear-optical methods of surface diagnostics (generation of second and third harmonics and difference frequencies in reflection, and Raman scattering of light). The high information content and sensitivity of these methods compared with other methods for studying surfaces is pointed out. The problem of the appearance of spatially periodic surface structures induced by laser radiation is examined. The theories of different laser-induced instabilities of the surface relief, giving rise to the formation of these structures (generation of surface acoustic and capillary waves and evaporation waves), are reviewed. Theoretical and experimental results are compared.