The article is a review of the basic papers on parametric antennas published in 1963--1977. Parametric antennas that make it possible to obtain low-frequency radiation of very high directivity with a small aperture of primary source have recently become a subject of active research. Progress in the theory now makes it possible to obtain all the basic characteristics of an antenna. In the review the main attention is given to the axial distribution of sound pressure and to the width of the directivity characteristic at low frequencies. One of the basic shortcomings of such an antenna is low efficiency of parametric transformation. It is noted that regimes close to saturation are as yet insufficiently studied. Optimization of antenna parameters is necessary for improvement of its efficiency. An analysis of the basic experimental results shows that laboratory models of antennas with the primary frequency range of 0.5--1.5 MHz are not optimal. This, probably, is responsible for their efficiency being 10 dB lower than the theoretical value. In the review there are noted important possibilities of applications of such antennas in the field of underwater research.