Single-nucleotide variants (SNVs) that are strongly associated with many genetic diseases and tumors are important both biologically and clinically. Detection of SNVs holds great potential for disease diagnosis and prognosis. Recent advances in DNA nanotechnology have offered numerous principles and strategies amenable to the detection and quantification of SNVs with high sensitivity, specificity, and programmability. In this review, we will focus our discussion on emerging techniques making use of DNA strand displacement, a basic building block in dynamic DNA nanotechnology. Based on their operation principles, we classify current SNV detection methods into three main categories, including strategies using toehold-mediated strand displacement reactions, toehold-exchange reactions, and enzyme-mediated strand displacement reactions. These detection methods discriminate SNVs from their wild-type counterparts through subtle differences in thermodynamics, kinetics, or response to enzymatic manipulation. The remarkable programmability of dynamic DNA nanotechnology also allows the predictable design and flexible operation of diverse strand displacement probes and/or primers. Here, we offer a systematic survey of current strategies, with an emphasis on the molecular mechanisms and their applicability to in vitro diagnostics.