Although genetic analysis has identified risk loci for many other common medical diseases (Hindorff et al., 2009), success has yet to visit MD. In this Review, we consider what has so far been learnt, consider reasons for the difficulties encountered, and propose how these might be overcome. We start by reviewing evidence from the genetic epidemiology literature relevant to the genetic basis of MD. We then consider what genome-wide association studies (GWASs) have told us. The GWAS results are particularly important for interpreting the large, forbidding literature on candidate gene studies, which we review next. In addition, GWAS findings inform us about the extent to which rare but more highly penetrant genetic variants might contribute to liability to MD. We finally examine whether there exist forms of MD that might be more genetically homogeneous and consider how these might be identified.