Population-scale analysis of genomic variation linked to individual-level data on disease, treatment and response, has the potential to answer many key questions in biomedical research about the biological processes that lead to disease and how best to design effective, and individualized interventions. However, the analysis of medical data obtained from routine sources and through self-reporting has many challenges. I will describe work using the UK Biobank data to characterize the genetic architecture and heterogeneity of common human diseases and discuss some of the many open statistical and computational challenges in the field.