This review discusses nonlinear acoustic phenomena which are analogous to corresponding phenomena in optics: self-interaction effects in acoustic beams, parametric effects, stimulated scattering of sound, wave-front (phase) conjugation of sound waves, and also techniques of active acoustic spectroscopy. The authors point out that these processes must evolve rather rapidly in space and time in order to avoid the formation of shock waves and the nonlinear dissipation of energy which accompanies them; this rapid evolution is provided by the interaction of sound with non-acoustic forms of fluid motion: convection, oscillating bubbles, and by thermal, hydrodynamic and concentration waves. Features which are peculiar to nonlinear acoustic phenomena are emphasized, i.e., the parametric mechanism for acoustic phase conjugation and the possibility of detecting stimulated acoustic scattering by single scatterers. The goal of the review is to draw additional attention to promising developments in nonlinear acoustics.