This paper outlines prospects for applying the emerging techniques of synthetic biology to the field of anatomy, with the aim of programming cells to organize themselves into specific, novel arrangements, structures and tissues. There are two main reasons why developing this hybrid discipline – synthetic morphology – would be useful. The first is that having a way to engineer self-constructing assemblies of cells would provide a powerful means of tissue engineering for clinical use in surgery and regenerative medicine. The second is that construction of simple novel systems according to theories of morphogenesis gained from study of real embryos will provide a means of testing those theories rigorously, something that is very difficult to do by manipulation of complex embryos. This paper sets out the engineering requirements for synthetic morphology, which include the development of a library of sensor modules, regulatory modules and effector modules that can be connected functionally within cells. A substantial number of sensor and regulatory modules already exist and this paper argues that some potential effector modules have already been identified. The necessary library may therefore be within reach. The paper ends by suggesting a set of challenges, ranging from simple to complex, the achievement of which would provide valuable proofs of concept.