In 1996, we began a research project on molecular computers under the new program “Research for the Future” funded by the Japan Society for the Promotion of Science. In this paper, we first summarize the research that has been completed in the field of DNA computing and the research problems that must be overcome. We also report some achievements of our research project in the first two years. We then propose a new direction in research towardsautonomous molecular computers, and describe the author’s work on the implementation of state machines using DNA molecules. We finally discuss the future perspectives on molecular computing based on our experiences.