Starting with the first single-molecule fluorescence experiments in 1990, the field of cryogenic single-molecule spectroscopy exploits the narrow zero-phonon lines of single molecules, usually in molecular crystals and glasses. Occasionally, similar experiments can also be done at room temperature, as illustrated by the case of the NV- center in diamond. In this review contribution, I shall illustrate the variety and scope of the experiments performed in the past 28 years, highlighting some important points and outlooks.