A coupled cell system is a network of interacting dynamical systems. Coupled cell models assume that the output from each node is important and that signals from two or more nodes can be compared so that patterns of synchrony can emerge. The principal question is: How does network architecture (who is talking to whom) affect the kinds of synchronous solutions that are expected in network equations. This talk will discuss a classification of rigid phase-shift synchrony in time-periodic solutions in such systems, as well as some curious synchrony-breaking bifurcations.