DNA (deoxyribonucleotide acids) computer is an emerging new study area that basically combines molecular biology study of DNA molecules and computational study on how to employ these specific molecules to calculate. In 1994 Adleman described his pioneering research on DNA computing in Science. This is the first experimental report on DNA computer study. In 2001 Benenson et al published a paper in Nature regarding a programmable and autonomous DNA computing device. Because of its Turing-like functions, the device is regarded as another milestone progress for DNA computer study. The main features of DNA computer are massively parallel computing ability and potential enormous data storage capacity. Comparing with conventional electronic computers, DNA molecules provide conceptually a revolution in computing, and more and more implications have been found in various disciplines. DNA computer studies have brought great progress not only in its own computing mechanisms, but also in DNA manipulation technologies especially nano-technology. This article presents the basic principles of DNA computer, its applications, its important relationship with genomic research and our comments on all above issues.