Over the last 5 to 6 years, genome-wide association studies (GWAS) have proved enormously successful for the detection of genomic regions that harbour genes associated with complex diseases and quantitative traits. However, moving from a replicable association signal to determination of the underlying causal genetic variant and an understanding of its mechanism has proved more challenging. The variants detected in GWAS generally confer modest effects (odds ratios of 1.5 or less), making them of limited use for risk prediction, and do not generally account for a large proportion of the observed heritability (the additive genetic contribution to the overall trait variance), suggesting there are many additional, possibly interacting, genetic contributors to be found. From a biological perspective, interactions between genes (epistasis) are expected to be ubiquitous, as complex biological phenotypes are likely to result from complex combinations of genetic (and non-genetic) factors rather than from such factors operating in isolation. In this talk I will discuss the statistical challenges involved in, and some possible strategies for, detecting and modelling gene-gene interactions using GWAS data. I will focus on some recent work carried out by ourselves and others to develop tests that show high power over a wide range of scenarios while maintaining an acceptable false positive rate.