Synthetic biology is an emerging research field, in which engineering principles are applied to natural, living systems. A major goal of synthetic biology is to harness the inherent “biological nanotechnology” of living cells for the purposes of computation, production or diagnosis. As the field evolves, it is gradually developing from a single-cell approach (akin to using standalone computers) to a distributed, population-based approach (akin to using networks of connected machines). We anticipate this eventually representing the “third wave” of synthetic biology (the first two waves being the emergence of modules and systems, respectively, with the second wave still yet to peak). In this paper, we review the developments that are leading to this third wave, and describe some of the existing scientific and technological challenges.