DNA nanotechnology has seen large developments over the last 30 years through the combination of solid phase synthesis and the discovery of DNA nanostructures. Solid phase synthesis has facilitated the availability of short DNA sequences and the expansion of the DNA toolbox to increase the chemical functionalities afforded on DNA, which in turn enabled the conception and synthesis of sophisticated and complex 2D and 3D nanostructures. In parallel, polymer science has developed several polymerization approaches to build di- and triblock copolymers bearing hydrophilic, hydrophobic, and amphiphilic properties. By bringing together these two emerging technologies, complementary properties of both materials have been explored; for example, the synthesis of amphiphilic DNA-polymer conjugates has enabled the production of several nanostructures, such as spherical and rod-like micelles. Through both the DNA and polymer parts, stimuli-responsiveness can be instilled. Nanostructures have consequently been developed with responsive structural changes to physical properties, such as pH and temperature, as well as short DNA through competitive complementary binding. These responsive changes have enabled the application of DNA-polymer conjugates in biomedical applications including drug delivery. This review discusses the progress of DNA-polymer conjugates, exploring the synthetic routes and state-of-the-art applications afforded through the combination of nucleic acids and synthetic polymers.