The main results of works on study of influence of nonlinearity on propagation of radio waves through metals placed in a constant magnetic field are described. The trapping of carriers by the magnetic field of a wave with a large amplitude leads to suppression of collisionless absorption and to a possibility of propagation in metals of waves of various types. In copper, the propagation of helicons becomes possible in the geometry when on the Fermi surface there are open orbits preventing from wave propagation. In zinc, in which the cyclotron absorption by holes exists for any wave lengths in the linear regime, the decrease of this absorption results in a possibility of propagation of an electron doppleron. In noble metals and metals of the Third Group, where any waves are absent in the linear regime, the propagation of nonlinear waves of the new type, which do not have counterparts in the linear regime, becomes possible in the range of weak fields. Multiple reflections of nonlinear waves from internal surfaces of a metallic plate lead to the formation of standing waves in a sample. In this case resonance maxima appear in a dependence of the surface resistance of the sample on a constant magnetic field. In the maxima the transparency coefficient of a metal with respect to radio emission can increase by one-two orders of magnitude.