Complex natural processes may often be expressed in terms of networks of computational components, such as Boolean logic gates or artificial neurons. The interaction of biological molecules and the flow of information controlling the development and behaviour of organisms is particularly amenable to this approach, and these models are well-established in the biological community. However, only relatively recently have papers appeared proposing the use of such systems to perform useful, human-defined tasks. Rather than merely using the network analogy as a convenient technique for clarifying our understanding of complex systems, it may now be possible to harness the power of such systems for the purposes of computation. In this paper we review several such proposals, focusing on the molecular implementation of fundamental computational elements.