DNA and RNA molecules possess precise recognition and powerful signal storage abilities. By exploiting their biological properties, it is possible to construct molecule-scale logic gates and realize logistic operations which, as an emerging multidisciplinary area between computer sciences and molecular biology, has intrigued great research attention. In this article, we summarize methods to construct logic gates by exploiting enzymatic and structural properties of DNA and RNA, and approaches to integrate logic gates into complex logistic operations. Finally, we introduce biomedical applications of DNA/RNA logic gates for in-vitro detection and in-vivo diagnosis and therapy.