The powerful self-assembly features of DNA make it a unique template to finely organize and control matter on the nanometre scale. While DNA alone offers a high degree of fidelity in its self-assembly, a new area of research termed 'supramolecular DNA assembly' has recently emerged. This field combines DNA building blocks with synthetic organic, inorganic and polymeric structures. It thus brings together the toolbox of supramolecular chemistry with the predictable and programmable nature of DNA. The result of this molecular partnership is a variety of hybrid architectures, that expand DNA assembly beyond the boundaries of Watson-Crick base pairing into new structural and functional properties. In this tutorial review we outline this emerging field of study, and describe recent research aiming to synergistically combine the properties inherent to DNA with those of a number of supramolecular scaffolds. This ultimately creates structures with numerous potential applications in materials science, catalysis and medicine.