The interaction between light and matter can be controlled efficiently by structuring materials at a length scale shorter than the wavelength of interest. With the goal to build optical devices that operate at the nanoscale, plasmonics has established itself as a discipline, where near-field effects of electromagnetic waves created in the vicinity of metallic surfaces can give rise to a variety of novel phenomena and fascinating applications. As research on plasmonics has emerged from the optics and solid-state communities, most laboratories employ top-down lithography to implement their nanophotonic designs. In this review, we discuss the recent, successful efforts of employing self-assembled DNA nanostructures as scaffolds for creating advanced plasmonic architectures. DNA self-assembly exploits the base-pairing specificity of nucleic acid sequences and allows for the nanometer-precise organization of organic molecules but also for the arrangement of inorganic particles in space. Bottom-up self-assembly thus bypasses many of the limitations of conventional fabrication methods. As a consequence, powerful tools such as DNA origami have pushed the boundaries of nanophotonics and new ways of thinking about plasmonic designs are on the rise.