A brief review is given of theoretical and experimental investigations of the spontaneous emission from an atom in a resonator cavity. A theory of spontaneous emission from a two-level atom in free space and in a cavity is presented in a methodical unified manner. In a single-mode resonator the structure of the spectrum of the emitted photons is a singlet or a doublet, depending on the ratio of the cavity damping to the constant of the interaction of an atom with a field. The emission spectrum of an atom in a cavity with two modes with similar frequencies may have a triplet structure.