As an emerging new research area, DNA computation, or more generally biomolecular computation, extends into other fields such as nanotechnology and material design, and is developing into a new sub-discipline of science and engineering. This paper provides a brief survey of some concepts and developments in this area. In particular several approaches are described for biomolecular solutions of the satisfiability problem (using bit strands, DNA tiles and graph self-assembly). Theoretical models such as the primer splicing systems as well as the recent model of forbidding and enforcing are also described. We review some experimental results of self-assembly of DNA nanostructures and nanomechanical devices as well as the design of an autonomous finite state machine.