There are many diseases whose causal tissues or cell types are unknown; identifying these tissues and cell types is critical for exploring gene regulatory mechanisms that may contribute to disease. One approach to identifying disease-relevant tissues and cell types is to use gene expression or epigenetic data to identify regions of the genome that are active in each candidate tissue or cell type, and then to use data from genome-wide association studies (GWAS) to test which of these sets of active regions is enriched for genetic signal for the disease. We describe a method called stratified LD score regression (S-LDSC) to do this enrichment analysis, based on a random effects model for GWAS data. We apply S-LDSC to 48 diseases and traits, testing the relevance of hundreds of candidate tissues and cell types for each disease or trait. We find many significant enrichments, including enrichments that recapitulate known biology (e.g., immune enrichment for immunological diseases) as well as new results (e.g. enrichment of inhibitory over excitatory neurons for bipolar disorder but excitatory over inhibitory neurons for schizophrenia).