Work in which electromagnetic excitations in metals and semimetals in a strong magnetic field have been studied is reviewed. For the analysis of the spectrum of the numerous electromagnetic excitations, the collisionless-damping regimes which determine the limits of the existence of weakly-damped excitations and make it possible to carry out a natural classification of the spectrum of electromagnetic waves in quantizing and classically-strong magnetic fields are derived with the aid of conservation laws. In addition, the collisionless-damping regimes give an intuitive picture of oscillatory effects in the propagation of other, nonelectromagnetic excitations. All types of quantum waves in electron and electron-hole plasmas and also the effect of magnetic quantization on the spectrum of the classical electromagnetic excitations, are considered in the review. The conditions for which quantum waves and oscillations of the damping of classical excitations can be observed are discussed. The last section of the review summarizes the results of work in which electromagnetic waves in metals with a complicated Fermi surface have been studied. The connection between the geometry of the Fermi surface and the spectrum of the electromagnetic normal modes is analyzed.