The main tenet of the neutral theory is that the great majority of evolutionary changes at the molecular level are caused not by Darwinian selection but by random fixation of selectively neutral (or very nearly neutral) alleles through random sampling drift under continued mutation pressure. The theory also asserts that the majority of protein and DNA polymorphisms are selectively neutral, and that they are maintained in the species by mutational input balanced by random extinction rather than by "balancing selection." The neutral theory is based on simple assumptions. This enabled us to develop mathematical theories (using the diffusion equation method) that can treat these phenomena in quantitative terms and that permit theory to be tested against actual observations. Although the neutral theory has been severely criticized by the neo-Darwinian establishment, supporting evidence has accumulated over the last 20 years. In particular, the recent burst of DNA sequence data helped to strengthen the theory a great deal. I believe that the neutral theory triggered reexamination of the traditional "synthetic theory of evolution." In this paper, I review the present status of the neutral theory, including discussions of such topics as "molecular evolutionary clock," very high evolutionary rates observed in RNA viruses, a deviant coding system found in Mycoplasm together with the concept of mutation-driven neutral evolution, and the origin of life. I also present a worldview based on the conception of what I call "survival of the luckiest."