This article examines the DNA-based self-assembly of nanostructures. It first reviews the development of DNA self-assembly and DNA-directed assembly, focusing on the main strategies and building blocks available in the modern molecular construction toolbox, including the design, construction, and analysis of nanostructures composed entirely of synthetic DNA, as well as origami nanostructures formed from a mixture of synthetic and biological DNA. In particular, it considers the stepwise covalent synthesis of DNA nanomaterials, unmediated assembly of DNA nanomaterials, hierarchical assembly, nucleated assembly, and algorithmic assembly. It then discusses DNA-directed assembly of heteromaterials such as proteins and peptides, gold nanoparticles, and multicomponent nanostructures. It also describes the use of complementary DNA cohesion as 'smart glue' for bringing together covalently linked functional groups, biomolecules, and nanomaterials. Finally, it evaluates the potential future of DNA-based self-assembly for nanoscale manufacturing for applications in medicine, electronics, photonics, and materials science.