A short history of the major features of neutral theories of molecular evolution is presented. Emphasis is placed on the nearly neutral theory, as this version of the neutral theory has explained the widest range of phenomena. The shift of interest from protein to DNA evolution is chronicled, leading to the modern view that silent and replacement substitutions are responding to different evolutionary forces. However, the exact nature and magnitude of these forces remains controversial, as all current theoretical models suffer either from assumptions that are not quite realistic or from an inability to account readily for all phenomena. Although the gathering of sequence data has been the main effort of contemporary population genetics, further exploration of theoretical models of molecular evolution would provide a more coherent framework for data analysis.