Nucleic acids are emerging as powerful and functional biomaterials due to their molecular recognition ability, programmability, and ease of synthesis and chemical modification. Various types of nucleic acids have been used as gene regulation tools or therapeutic agents for the treatment of human diseases with genetic disorders. Nucleic acids can also be used to develop sensing platforms for detecting ions, small molecules, proteins, and cells. Their performance can be improved through integration with other organic or inorganic nanomaterials. To further enhance their biological properties, various chemically modified nucleic acid analogues can be generated by modifying their phosphodiester backbone, sugar moiety, nucleobase, or combined sites. Alternatively, using nucleic acids as building blocks for self-assembly of highly ordered nanostructures would enhance their biological stability and cellular uptake efficiency. In this review, we will focus on the development and biomedical applications of structural and functional natural nucleic acids, as well as the chemically modified nucleic acid analogues over the past ten years. The recent progress in the development of functional nanomaterials based on self-assembled DNA-based platforms for gene regulation, biosensing, drug delivery, and therapy will also be presented. We will then summarize with a discussion on the advanced development of nucleic acid research, highlight some of the challenges faced and propose suggestions for further improvement.