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Epidemic models are always simplifications of real world epidemics. Which real world features to include, and which simplifications to make, depend both on the disease of interest and on the purpose of the modelling. In the present paper we discuss some such purposes for which a stochastic model is preferable to a deterministic counterpart. The two main examples illustrate the importance of allowing the infectious and latent periods to be random when focus lies on the probability of a large epidemic outbreak and/or on the initial speed, or growth rate, of the epidemic. A consequence of the latter is that estimation of the basic reproduction number R(0) is sensitive to assumptions about the distributions of the infectious and latent periods when using data from the early stages of an outbreak, which we illustrate with data from the H1N1 influenza A pandemic. Some further examples are also discussed as are some practical consequences related to these stochastic aspects.