A coupled cell system is a collection of interacting dynamical systems. Coupled cell models assume that the output from each cell is important and that signals from two or more cells can be compared so that patterns of synchrony can emerge. We ask: How much of the qualitative dynamics observed in coupled cells is the product of network architecture and how much depends on the specific equations? Speficially we study the structure of synchrony-breaking bifurcations in these systems. The ideas will be illustrated through a series of examples and theorems. One example shows how a frequency filter / amplifier can be built from a small three-cell feed forward network; and a second illustrates patterns of synchrony in lattice dynamical systems. One theorem gives necessary and sufficient conditions for synchrony in terms of network architecture; and a second shows that synchronous dynamics may itself be viewed as dynamics in a coupled cell system through a quotient construction.