Approximate Bayesian Computation (ABC) and other simulationbased inference methods are becoming increasingly used for inference in complex systems, due to their relative ease-of-implementation. We briefly review some of the more popular variants of ABC and their application in epidemiology, before using a real-world model of HIV transmission to illustrate some of challenges when applying ABC methods to high-dimensional, computationally intensive models.We then discuss an alternative approach- history matching-that aims to address some of these issues, and conclude with a comparison between these different methodologies.