Genome-wide association studies (GWAS) aim to identify genetic factors associated with phenotypes. Standard analyses test variants for associations individually. However, variant-level associations are hard to identify and can be difficult to interpret biologically. Enrichment analyses help address both problems by targeting sets of biologically related variants. Here we introduce a new model-based enrichment method that requires only GWAS summary statistics. Applying this method to interrogate 4,026 gene sets in 31 human phenotypes identifies many previously-unreported enrichments, including enrichments of endochondral ossification pathway for height, NFAT-dependent transcription pathway for rheumatoid arthritis, brain-related genes for coronary artery disease, and liver-related genes for Alzheimer's disease. A key feature of our method is that inferred enrichments automatically help identify new trait-associated genes. For example, accounting for enrichment in lipid transport genes highlights association between MTTP and low-density lipoprotein levels, whereas conventional analyses of the same data found no significant variants near this gene.