In nature, DNA molecules carry the hereditary information. But DNA has physical and chemical properties that make it attractive for uses beyond heredity. In this Review, we discuss the potential of DNA for creating machines that are both encoded by and built from DNA molecules. We review the main methods of DNA nanostructure assembly, describe recent advances in building increasingly complex molecular structures and discuss strategies for creating machine-like nanostructures that can be actuated and move. We highlight opportunities for applications of custom DNA nanostructures as scientific tools to address challenges across biology, chemistry and engineering.