A coupled cell system is a collection of individual, but interacting, dynamical systems. Coupled cell models assume that the output from each cell is important not just the dynamics considered as a whole. In these systems the signals from two or more cells can be compared and patterns of activity can emerge. We ask when can the cell dynamics in a subset of cells be identical (synchrony) or differ just by a phase shift. In general: How much of the dynamics observed in coupled cells is the product of network architecture and how much is related to the specific dynamics of cells and the specific way they are coupled?
We illustrate the ideas through a series of examples and discuss three theorems. The first result classifies spatio-temporal symmetries of periodic solutions; the second gives necessary and sufficient conditions for robust synchrony in terms of network architecture; and the third shows that synchronous dynamics may itself be viewed as a coupled cell system through a quotient construction.