Epidemic models are developed as a means of gaining understanding about the dynamics of the spread of infection (human and animal pathogens, computer viruses etc.) and of rumours and other information. This understanding can then inform control measures to limit, or in some cases enhance, spread. Towards this goal, I will start from some simple stochastic transmission models, and describe some Gaussian approximations and their use for inference illustrating this with data from a norovirus outbreak as well as from simulations. I will then discuss ways of incorporating population structure via metapopulations and networks, and the effects of network structure on epidemic spread. Finally I will briefly consider the extension to explicitly spatial mobile networks, as for example when computer viruses spread via short-range wireless or bluetooth connections.