<p>We present a brief review of theoretical and numerical works on three-dimensional acoustic turbulence both in a weakly nonlinear regime, when the amplitudes of sound waves are small, and in the case of strong nonlinearity. This review is based on the classical studies on weak acoustic turbulence by V. E. Zakharov and R. Z. Sagdeev [1, 2], on the one hand, and by B. B.Kadomtsev and V. I. Petviashvili on the other hand [3]. Until recently, there have been no convincing numerical experiments confirming one or the other point of view. In works [4, 5] by the authors of this review, strong arguments were found based on direct numerical simulation in favor of both theories. It is shown that the spectrum of weak Zakharov–Sagdeev turbulence ∝ <i>k</i>^-3/2 is realized not only at low positive dispersion of sound waves, but also in the case of complete absence of dispersion. The calculated turbulence spectra in the weakly nonlinear regime have anisotropic distribution: in the region of small k, narrow cones (jets), broadening in the Fourier space, are formed. In the case of weak dispersion, the jets are smoothed out, and the turbulence spectrum tends to be isotropic in the region of short wavelengths. In the absence of dispersion, the turbulence spectrum is a discrete set of jets subject to diffraction divergence. It is found that for each individual jet, nonlinear effects are much weaker than diffraction ones, which prevents the formation of shock waves. Thus, the spectra of weak Zakharov–Sagdeev turbulence are realized due to the smallness of nonlinear effects compared with dispersion or diffraction. As the pumping level increases in the dispersionless regime, when nonlinear effects start to dominate, shock waves, namely, discontinuities propagating in space, are formed. As a result, acoustic turbulence passes into a strongly nonlinear state in the form of an ensemble of random shock waves described by the Kadomtsev–Petviashvili spectrum decaying by the law ∝ <i>k</i>^-2.</p>