Likelihood-based inference for disease outbreak data can be very challenging due to the inherent dependence of the data and the fact that they are usually incomplete. In this paper we review recent Approximate Bayesian Computation (ABC) methods for the analysis of such data by fitting to them stochastic epidemic models without having to calculate the likelihood of the observed data. We consider both non-temporal and temporal-data and illustrate the methods with a number of examples featuring different models and datasets. In addition, we present extensions to existing algorithms which are easy to implement and provide an improvement to the existing methodology. Finally, R code to implement the algorithms presented in the paper is available on https://github.com/kypraios/epiABC.
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