In sharp contrast to the Darwinian theory of evolution by natural selection, the neutral theory claims that the overwhelming majority of evolutionary changes at the molecular level are caused by random fixation (due to random sampling drift in finite populations) of selectively neutral (i.e., selectively equivalent) mutants under continued inputs of mutations. The theory also asserts that most of the genetic variability within species at the molecular level (such as protein and DNA polymorphism) are selectively neutral or very nearly neutral and that they are maintained in the species by the balance between mutational input and random extinction. The neutral theory is based on simple assumptions, enabling us to develop mathematical theories based on population genetics to treat molecular evolution and variation in quantitative terms. The theory can be tested against actual observations. Neo-Darwinians continue to criticize the neutral theory, but evidence for it has accumulated over the last two decades. The recent outpouring of DNA sequence data has greatly strengthened the theory. In this paper, I review some recent observations that strongly support the neutral theory. They include such topics as pseudoglobin genes of the mouse, alpha A-crystallin genes of the blind mole rat, genes of influenza A virus and nuclear vs. mitochondrial genes of fruit flies. I also discuss such topics as the evolution of deviant coding systems in Mycoplasma, the origin of life and the unified understanding of molecular and phenotypic evolution. I conclude that since the origin of life on Earth, neutral evolutionary changes have predominated over Darwinian evolutionary changes, at least in number.