Adenoid cystic carcinomas (ACCs) are among the most enigmatic of human malignancies. These aggressive salivary gland cancers frequently recur and metastasize despite definitive treatment, with no known effective chemotherapy regimen. Here we determined the ACC mutational landscape and report the exome or whole-genome sequences of 60 ACC tumor-normal pairs. These analyses identified a low exonic somatic mutation rate (0.31 non-silent events per megabase) and wide mutational diversity. Notably, we found mutations in genes encoding chromatin-state regulators, such as SMARCA2, CREBBP and KDM6A, suggesting that there is aberrant epigenetic regulation in ACC oncogenesis. Mutations in genes central to the DNA damage response and protein kinase A signaling also implicate these processes. We observed MYB-NFIB translocations and somatic mutations in MYB-associated genes, solidifying the role of these aberrations as critical events in ACC. Lastly, we identified recurrent mutations in the FGF-IGF-PI3K pathway (30% of tumors) that might represent new avenues for therapy. Collectively, our observations establish a molecular foundation for understanding and exploring new treatments for ACC.