The availability of affordable high throughput technology for parallel genotyping has opened the field of genetics to genome-wide association studies (GWAS), and in the last few years hundreds of articles reporting results of GWAS for a variety of heritable traits have been published. What do these results tell us? Although GWAS have discovered a few hundred reproducible associations, this number is underwhelming in relation to the huge amount of data produced, and challenges the conjecture that common variants may be the genetic causes of common diseases. We argue that the massive amount of genetic data that result from these studies remains largely unexplored and unexploited because of the challenge of mining and modeling enormous data sets, the difficulty of using nontraditional computational techniques and the focus of accepted statistical analyses on controlling the false positive rate rather than limiting the false negative rate. In this article, we will review the common approach to analysis of GWAS data and then discuss options to learn more from these data. We will use examples from our ongoing studies of sickle cell anemia and also GWAS in multigenic traits.