There is considerable attention directed at chemically modifying nucleic acids with robust functional groups in order to alter their properties. Since the breakthrough of copper-assisted azide-alkyne cycloadditions (CuAAC), there have been several reports describing the synthesis and properties of novel triazole-modified nucleic acid derivatives for potential downstream DNA- and RNA-based applications. This review will focus on highlighting representative novel nucleic acid molecular structures that have been synthesized via the “click” azide-alkyne cycloaddition. Many of these derivatives show compatibility for various applications that involve enzymatic transformation, nucleic acid hybridization, molecular tagging and purification, and gene silencing. The details of these applications are discussed. In conclusion, the future of nucleic acid analogues functionalized with triazoles is promising.