DNA nanotechnology entails the construction of specific geometrical and topological targets from DNA. The goals include the use of DNA molecules to scaffold the assembly of other molecules, particularly in periodic arrays, with the objects of both crystal facilitation and memory-device construction. Many of these products are based on branched DNA motifs. DNA molecules with the connectivities of a cube and a truncated octahedron have been prepared. A solid-support methodology has been developed to construct DNA targets. DNA trefoil and figure-8 knots have been made, predicated on the relationship between a topological crossing and a half-turn of B-DNA or Z-DNA. The same basis has been used to construct Borromean rings from DNA. An RNA knot has been used to demonstrate an RNA topoisomerase activity. The desire to construct periodic matter held together by DNA sticky ends has resulted in a search for stiff components; DNA double crossover molecules appear to be the best candidates. It appears that novel DNA motifs may be of use in the new field of DNA-based computing.