One of the crucial challenges in nanoscience is gaining control over the formation of the desired nanoscale structures. Such structural control provides access to the novel material functions. While many functional nanoscale blocks are inorganic, soft matter components, i.e. surfactants, macromolecules, polymers, and biopolymers, can play an important role in defining structures formed from those blocks via self-assembly. In recent years DNA-based self-assembly approaches emerged as powerful means for nanoscale fabrications: DNA can direct inter-particle binding, can be used as a scaffold for particle positioning and can regulate a structural self-assembly. We review here the major areas of DNA-based nanoscale self-assembly, including systems formed purely from the DNA strands and structures formed by particles with the help of DNA. The methods for particles functionalized with DNA are elaborated. The assembly approaches that exploit DNA programmability for the creation of desired clusters, lattices and dynamically tunable systems are discussed.