The author had the pleasure of being involved in the pioneering experiments on sound wave propagation in the turbulent atmosphere (1939--1950). The obtained results were interpreted from the point of view of the, then recently developed, Kolmogorov--Obukhov (KO) statistical theory of locally isotropic turbulence. These results were one of the first confirmations of this theory. It may be said that the KO theory and the experiments mentioned above had stimulated the broad developments in the problem of ``waves and turbulence.'' The resulting classical theory now provides a basis for the analysis of signals and the computer simulation of sound propagation through turbulence. This paper provides an historical overview of the development of the classical theory for sound propagation through turbulent media. Models of turbulence and experimental verification of these models will be discussed for sound propagation in the atmosphere, as well as in seismic and underwater media. Some examples of the problem of ``wave turbulence and nonlinearity'' also will be discussed.