Higher organisms are complex, and their developmental processes are controlled by the sequential expression of genes that often form multigene families. Facts are surveyed on how functional diversity of genes is related to duplication of genes or segments of genes, by emphasizing that diversity is often enhanced by alternate splicing and proteolytic cleavage involving duplicated genes or gene segments. Analyses of a population genetics model for the origin of gene families suggest that positive Darwinian selection is needed for acquiring gene families with desirable functions. Based on these considerations, examples that show acceleration of amino acid substitution relative to synonymous change during evolutionary processes are surveyed. Some of such examples strongly suggest that positive selection has worked. In other cases it is difficult to judge whether or not acceleration is caused by positive Darwinian selection. As a general pattern, acceleration of amino acid substitution is often found to be related to gene duplication. It is thought that complexity and diversity of gene function have been advantageous in the long evolutionary course of higher organisms.