Acoustooptical phenomenon was anticipated theoretically by L. Brillouin in 1922. These anticipations were confirmed experimentally 10 years later. In the following years the influence of elastic wave on light wave propagation was described from many points of view, examined experimentally, and applied in practice. The first works describe interaction of unlimited plane waves but the fundamental meaning for practical applications has the description of real wave beams" interaction. This problem still exists despite huge progress made in acoustooptical phenomenon"s investigations. Among numerous description methods applicable to various, specific acoustooptical interactions are also such ones, that make it possible to describe interaction of beams of arbitrary spatial distributions. However, in today"s applications of acoustooptical phenomenon such as modulators, filters, spectrum analyzers, etc. one uses mostly laser light. Light beams emitted by laser may in many cases be described as gaussian beams. It means, that the correct description of acoustooptical interaction involving optical gaussian beams has significant practical meaning. This paper presents the review of theoretical works describing acoustooptical interaction between optical gaussian beams and acoustical waves. Special attention has been paid the application of complex geometrical optics" methods.© (2005) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.