Approximate Bayesian Computation (ABC) methods have become a “mainstream” statistical technique in the past decade, following the realisation by statisticians that they are a special type of non-parametric inference. In this survey of ABC methods, we focus on the recent literature, building on the previous survey of Marin et al. Stat Comput 21(2):279–291, 2011, [39]. Given the importance of model choice in the applications of ABC, and the associated difficulties in its implementation, we also give emphasis to this aspect of ABC techniques.