This paper addresses two main aspects of DNA computing research: DNA computing in vitro and in vivo. We first present a model of DNA computation developed in [5]: the circular insertion/deletion system. We review the result obtained in [5] stating that this system has the computational power of a Turing machine, and present the outcome of a molecular biologylab oratoryex periment from [5] that implements a small instance of such a system. This shows that rewriting systems of the circular insertion/deletion type are viable alternatives in DNA computation in vitro. In the second half of the paper we address DNA computing in vivo by presenting a model proposed in [17] and developed in [18] for the homologous recombinations that take place during gene rearrangement in ciliates. Such a model has universal computational power which indicates that, in principle, some unicellular organisms may have the capacity to perform any computation carried out by an electronic computer.