The existence of two sounds of different natures in the superfluid liquid is one of the best known and most thoroughly investigated properties of helium. An enormous mass of experimental and theoretical material on wave processes in helium has accumulated during the years that have passed since the discovery of second sound. Interest in these problems has especially increased in the last decade, first, because of the discovery of third and fourth sound (oscillations that propagate when the normal component of the liquid is clamped), and second, because of the possibility of investigating ultrashort sound waves by neutron and photon scattering. In this article the fundamental theoretical concepts and experimental results concerning the propagation of sound waves of the several types in superfluid liquid (in He$^4$ and He$^3$--He$^4$ solutions) are reviewed. Much attention is given to quantitative, as well as qualitative, comparison of the experimental results with theory. The bibliography has been made as complete as possible. The following topics are not discussed, although they touch directly upon the subject under review: the propagation of sound near the lambda point, the passage of waves across liquid-liquid and liquid-vapor interfaces, and the propagation of large-amplitude sound waves.