We survey the current status of single-molecule spectroscopy in the view point of theoretical aspects. After an explanation of basic concepts in single-molecule spectroscopy, we focus on the following topics: (1) line shape phenomena in disordered media, (2) photon counting statistics for time-dependent fluctuations in single-molecule spectroscopy, (3) fluorescence intensity fluctuations for nonergodic systems, (4) time-resolved single-molecule fluorescence for conformational dynamics of single biomolecules, (5) single-molecule reaction dynamics at room temperature, and (6) quantum jump method of single quantum system. We conclude this paper with some open questions and perspectives of single-molecule spectroscopy.