Unusual motifs of DNA present an extremely favorable construction medium: The sticky-ended association of DNA molecules occurs with high specificity, and it results in the formation of BDNA, whose structure is well known. The use of stable branched DNA molecules permits one to make stick-figures. We have used this strategy to construct a covalently closed DNA molecule whose helix axes have the connectivity of a cube, and a second molecule, whose helix axes have the connectivity of a truncated octahedron. In addition to branching topology, DNA also affords control of linking topology, because double helical half-turns of B-DNA or Z-DNA can be equated, respectively, with negative or positive crossings in topological objects. Consequently, we have been able to use DNA to make trefoil knots of both signs and figure-8 knots. DNA-based topological control has also led to the construction of Borromean rings. The key feature previously lacking in DNA construction has been a rigid molecule. We have discovered that antiparallel DNA double crossover molecules can provide this capability. We have incorporated these components in DNA assemblies that make use of this rigidity to achieve control on the geometrical level, as well as on the topological level. Rigid components have allowed us to construct a nanomechanical device, predicated on a DNA structural transition.