Annotating the molecular basis of human disease remains an unsolved challenge, as 93% of disease loci are non-coding and gene-regulatory annotations are highly incomplete1-3. Here we present EpiMap, a compendium comprising 10,000 epigenomic maps across 800 samples, which we used to define chromatin states, high-resolution enhancers, enhancer modules, upstream regulators and downstream target genes. We used this resource to annotate 30,000 genetic loci that were associated with 540 traits4, predicting trait-relevant tissues, putative causal nucleotide variants in enriched tissue enhancers and candidate tissue-specific target genes for each. We partitioned multifactorial traits into tissue-specific contributing factors with distinct functional enrichments and disease comorbidity patterns, and revealed both single-factor monotropic and multifactor pleiotropic loci. Top-scoring loci frequently had multiple predicted driver variants, converging through multiple enhancers with a common target gene, multiple genes in common tissues, or multiple genes and multiple tissues, indicating extensive pleiotropy. Our results demonstrate the importance of dense, rich, high-resolution epigenomic annotations for the investigation of complex traits.