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During the past decade, genome-wide association studies (GWAS) have been used to successfully identify tens of thousands of genetic variants associated with complex traits and diseases. These studies have produced extensive repositories of genetic variation and trait measurements across large numbers of individuals, providing tremendous opportunities for further analyses. However, privacy concerns and other logistical considerations often limit access to individual-level genetic data, motivating the development of methods that analyse summary association statistics. Here, we review recent progress on statistical methods that leverage summary association data to gain insights into the genetic basis of complex traits and diseases.