Optical spectroscopy at the ultimate limit of a single molecule has grown over the past dozen years into a powerful technique for exploring the individual nanoscale behavior of molecules in complex local environments. Observing a single molecule removes the usual ensemble average, allowing exploration of hidden heterogeneity in complex condensed phases as well as direct observation of dynamical state changes arising from photophysics and photochemistry, without synchronization. This paper reviews single-molecule spectroscopy experiments of the Moerner group, both at liquid helium temperatures and at room temperature, in the areas of physical chemistry, quantum optics, and biophysics. Due to the breadth of applications now appearing, single-molecule spectroscopy may be viewed as a useful new tool for the study of dynamics in complex systems.