Enormous data collection efforts and improvements in technology have made large-scale genome-wide association studies (GWAS) a promising approach to better understanding the genetics of common, complex diseases. However, the limited success of these studies so far suggests that genetic susceptibility may be due to a combined effect of multiple genetic variants (or interactions between variants), and that there may be a significant amount of genetic heterogeneity among those affected with complex diseases. New data analysis methods are needed to address these hypotheses.