Experimental and theoretical studies of high-frequency excitations in solids by $\gamma$-resonance spectroscopy are reviewed. Both the resonance-type and non-resonance-type alterations in M\"ossbauer spectra that are produced by high-frequency ac fields are elucidated. A considerable part of the review is devoted to problems of modulation of $\gamma$ radiation by ultrasonic vibrations. Various mechanisms of exciting sound by a radiofrequency field are studied, in particular, magnetostriction in ferromagnets. A new effect found by $\gamma$–resonance spectroscopy is discussed: collapse of the hyperfine structure upon fast remagnetization of a ferromagnet. A number of new nonlinear resonance phenomena are discussed that amount to combining the M\"ossbauer effect with the methods of radiospectroscopy (NMR, EPR, etc.). The possibility is discussed of applying these phenomena for studying the properties of solids.