In this talk I will develop a framework in which the computational power of multicellular systems can be distinguished from that of single celled systems. Put simply, under reasonable assumptions, single cells are likely limited to finite state, whereas multicellular systems can much more easily take advantage of arbitrarily large state spaces. The arguments are constructive and practicable: I will describe experiments in synthetic gene networks, cell-to-cell communication, programmed cell-death, and growth control that provide a palette of basic operations that can in principle be composed in to the following computational devices. Finite state machines in single cells; Turing Machines in spatial arrangements of multiple cells; Parallelized Register Machines in well mixed consortia of multiple cells. Theoretical results, simulations, and preliminary experiments aimed at realizing such computations will be discussed.