The results of investigations of nonlinear waves of first and second sound in HeII are reviewed. The equations of hydrodynamics of HeII in the standard and Hamiltonian formulations are presented. One-dimensional nonlinear waves and effects such as nonlinear conversion of waves into one another, formation of shock fronts, renormalization of the velocity of sound, and others are described. The effect of damping and dispersion is studied. A description of multidimensional waves is followed by a description of the phenomenon of self-focusing. Next, stability is discussed, the solution of the problem of the stability of a pressure shock wave is presented, and stochastic wave processes in acoustic turbulence are discussed. Experimental investigations of nonlinear waves in HeII are presented. In conclusion the paths for further development of the problems touched upon are discussed.