Synthetic biology uses interchangeable and standardized "bio-parts" to construct complex genetic networks that include sensing, information processing and effector modules: these allow robust and tunable transgene expression in response to a change in signal input. The rise of this field has coincided closely with the emergence of regenerative medicine as a distinct discipline. Unlike synthetic biology, regenerative medicine uses the natural abilities of cells to make trophic factors and to produce new tissues as they would in normal development and tissue maintenance. In this article, we argue that bringing these young fields together, so that synthetic biology techniques are applied to the problem of regeneration, has the potential significantly to enhance our ability to help those in clinical need. We first review the synthetic tool kit available for engineered mammalian networks, then examine the main areas in which synthetic biology techniques might be applied to promote regeneration: (i) biosynthesis and controlled release of therapeutic molecules, (ii) synthesis of scaffold material, (iii) regulation of stem cells, and (iv) programming cells to organize themselves into novel tissues. We finally consider the long-term potential of synthetic biology for regenerative medicine, and the risks and challenges ahead.