The acoustic radiation pressure has found practical application in recent years in instruments measuring sound intensity and in experiments on acoustic levitation. The concept of radiation pressure has, however, long fascinated both optical and acoustical physicists. The history of light radiation pressure goes back more than 200 years to Leonhard Euler, while the concept of acoustic radiation pressure dates from the time and work of Rayleigh. It was pointed out by Brillouin that what we call radiation pressure is not a pressure at all, but a diagonal tensor, all the diagonal terms of which are not identical. The size of the effect is small, and the values obtained for the radiation pressure are very sensitive to boundary conditions and to the approximations that must necessarily be employed. In addition, although the phenomenon is primarily one of nonlinear acoustics, it can be observed down to the lowest sound intensities under certain conditions. Thus, the Rayleigh radiation pressure vanishes for the linear case, but the usually measured Langevin pressure does not. It might be said that radiation pressure is a phenomenon that the observer thinks he understands—for short intervals, and only every now and then.