To help elucidate genetic variants underlying complex traits, we develop EpiMap, a compendium of 833 reference epigenomes across 18 uniformly-processed and computationally-completed assays. We define chromatin states, high-resolution enhancers, activity patterns, enhancer modules, upstream regulators, and downstream target gene functions. We annotate 30,247 genetic variants associated with 534 traits, recognize principal and partner tissues underlying each trait, infer trait-tissue, tissue-tissue and trait-trait relationships, and partition multifactorial traits into their tissue-specific contributing factors. Our results demonstrate the importance of dense, rich, and high-resolution epigenomic annotations for complex trait dissection, and yield numerous new insights for understanding the molecular basis of human disease.