Both drift and selection are important for nucleotide substitutions in evolution. The nearly neutral theory was developed to clarify the effects of these processes. In this article, the nearly neutral theory is presented with special reference to the nature of weak selection. The mean selection coefficient is negative, and the variance is dependent on the environmental diversity. Some facts relating to the theory are reviewed. As well as nucleotide substitutions, illegitimate recombination events such as duplications, deletions and gene conversions leave indelible marks on molecular evolution. Gene duplication and conversion are sources of the evolution of new gene functions. Positive selection is necessary for the evolution of novel functions. However, many examples of current gene families suggest that both drift and selection are at work on their evolution.