The neutral theory of molecular evolution has been widely accepted and is the guiding principle for studying evolutionary genomics and the molecular basis of phenotypic evolution. Recent data on genomic evolution are generally consistent with the neutral theory. However, many recently published papers claim the detection of positive Darwinian selection via the use of new statistical methods. Examination of these methods has shown that their theoretical bases are not well established and often result in high rates of false-positive and false-negative results. When the deficiencies of these statistical methods are rectified, the results become largely consistent with the neutral theory. At present, genome-wide analyses of natural selection consist of collections of single-locus analyses. However, because phenotypic evolution is controlled by the interaction of many genes, the study of natural selection ought to take such interactions into account. Experimental studies of evolution will also be crucial.