It is known that, in comparison with homogeneous media (e.g., water, air), acoustical nonlinearity of a liquid with a small concentration of bubbles can be anomalously high. The influence of bubbles upon nonlinear properties of the medium is often much more significant than the simultaneous change of linear characteristics, such as sound speed. This paper presents a brief review of our investigations of nonlinear acoustic phenomena in bubble clouds, and some results concerning nonlinear acoustic methods of measurements of bubble radii and their distribution in water. (1) The theory of the bubble medium is based on summation of the fields scattered by separate bubbles. The scattered field consists of coherent and noncoherent parts, and the latter can be treated as a nonlinear reverberation signal which takes place at frequencies different from those of the incident acoustic wave: second harmonics in the case of a harmonic primary radiator, and sum- and difference-frequency signals for a bifrequency radiator. The formulas relating these signals to the bubble distribution in the layer have been obtained. (2) To observe nonlinear acoustic effects in a subsurface bubble layer and in sea sediments, two echosounders working at different frequencies were used. The sum- and difference-frequency components were observed in the signals scattered from sediments with bubbles and from the subsurface bubble layer. The theory of such nonlinear scattering is in good agreement with experimental data.