The field of structural DNA nanotechnology aims at the systematic development of self-assembling nanostructures using DNA as the construction material. Research in this area is progressing rapidly, and the controlled, computer-aided design of increasingly complex structures is becoming feasible. One thread of this endeavour is the design and characterisation of self-assembling 3D nanostructures based on wireframe polyhedral models. This article aims to illustrate some of the key developments in this direction, in sufficient detail so that the reader can achieve a general understanding of the main concepts and approaches. The emphasis is on the design principles rather than experimental methodology, and the role of computer science and computational tools is set forth.