Charles Darwin proposed that evolution occurs primarily by natural selection, but this view has been controversial from the beginning. Two of the major opposing views have been mutationism and neutralism. Early molecular studies suggested that most amino acid substitutions in proteins are neutral or nearly neutral and the functional change of proteins occurs by a few key amino acid substitutions. This suggestion generated an intense controversy over selectionism and neutralism. This controversy is partially caused by Kimura's definition of neutrality, which was too strict (|2Ns|< or =1). If we define neutral mutations as the mutations that do not change the function of gene products appreciably, many controversies disappear because slightly deleterious and slightly advantageous mutations are engulfed by neutral mutations. The ratio of the rate of nonsynonymous nucleotide substitution to that of synonymous substitution is a useful quantity to study positive Darwinian selection operating at highly variable genetic loci, but it does not necessarily detect adaptively important codons. Previously, multigene families were thought to evolve following the model of concerted evolution, but new evidence indicates that most of them evolve by a birth-and-death process of duplicate genes. It is now clear that most phenotypic characters or genetic systems such as the adaptive immune system in vertebrates are controlled by the interaction of a number of multigene families, which are often evolutionarily related and are subject to birth-and-death evolution. Therefore, it is important to study the mechanisms of gene family interaction for understanding phenotypic evolution. Because gene duplication occurs more or less at random, phenotypic evolution contains some fortuitous elements, though the environmental factors also play an important role. The randomness of phenotypic evolution is qualitatively different from allele frequency changes by random genetic drift. However, there is some similarity between phenotypic and molecular evolution with respect to functional or environmental constraints and evolutionary rate. It appears that mutation (including gene duplication and other DNA changes) is the driving force of evolution at both the genic and the phenotypic levels.