Plasticity in neural circuits can result from alterations in synaptic strength or connectivity, as well as from changes in the excitability of the neurons themselves. To better understand the role of plasticity in the brain, we need to establish how brain circuits work and the kinds of computations that different circuit structures achieve. By linking theoretical and experimental studies, we are beginning to reveal the consequences of plasticity mechanisms for network dynamics, in both simple invertebrate circuits and the complex circuits of mammalian cerebral cortex.