Recent advances in the understanding of the dynamics of populations of spiking neurones are reviewed. These studies shed light on how a population of neurones can follow arbitrary variations in input stimuli, how the dynamics of the population depends on the type of noise, and how recurrent connections influence the dynamics. The importance of inhibitory feedback for the generation of irregularity in single cell behaviour is emphasized. Examples of computation that recurrent networks with excitatory and inhibitory cells can perform are then discussed. Maintenance of a network state as an attractor of the system is discussed as a model for working memory function, in both object and spatial modalities. These models can be used to interpret and make predictions about electrophysiological data in the awake monkey.