This thesis starts from the assumption that individual neuronal action potentials (spikes) have computational and dynamical significance. Two of the types of activity that networks of spiking neurons can engage in are sequences and synchrony. The first part of the work reviews the role spikes, sequences and synchrony play in coding, dynamics and learning in the nervous system and models of the nervous system. Models of spiking neurons, especially the spike response model (SRM), feature strongly, as do synfire chains, a form of spatiotemporal sequence. A methodology chapter deals with the problem of efficient simulation of networks of threshold-fire neurons such as integrate-and-fire (IF) neurons and SRM neurons. I show that networks of SRM neurons can be simulated with larger time steps than are required for numerical integration of equivalent networks of IF neurons. I extend an introduction method for more accurate simulation of IF neurons to noiseless and stochastically-firing SRM neurons, and show that a network of noiseless, interpolated SRM neurons can be simulated with larger time step than the equivalent network of interpolated IF neurons. Synfire chains can be learned with a temporal learning rule and a supervised training protocol. I extend previous analyses of the speed of recall of a synfire chain by (a) explicitly including the speed at which the synfire chain was trained and (b) performing an analysis on a synfire chain comprising discrete neurons rather than starting from a continuum approximation. I conclude that synfire chains can be recalled much faster than the speed at which they were trained.