We consider the problem of controlling false discoveries in association studies. We assume that the design of the study is adequate so that the “false discoveries” are potentially only because of random chance, not to confounding or other flaws. Under this premise, we review the statistical framework for hypothesis testing and correction for multiple comparisons. We consider in detail the currently accepted strategies in linkage analysis. We then examine the underlying similarities and differences between linkage and association studies and document some of the most recent methodological developments for association mapping.