The period from the 1950s to the 1970s proved to be extremely fruitful in the history of studies of nonlinear wave processes. This was largely due to the creation of powerful radio, optical and acoustic emitters. The paper briefly reviews the development of studies on nonlinear acoustics in the USSR during the said period, including the most significant achievements in the development of theory and creation of parametric arrays. The contribution of scientists such as N. N. Andreev, R. V. Khokhlov, O. V. Rudenko, V. A. Krasilnikov. V. A. Zverev, V. I. Timoshenko, etc. is acknowledged.