The Cancer Genome Atlas profiled 279 head and neck squamous cell carcinomas (HNSCCs) to provide a comprehensive landscape of somatic genomic alterations. Here we show that human-papillomavirus-associated tumours are dominated by helical domain mutations of the oncogene PIK3CA, novel alterations involving loss of TRAF3, and amplification of the cell cycle gene E2F1. Smoking-related HNSCCs demonstrate near universal loss-of-function TP53 mutations and CDKN2A inactivation with frequent copy number alterations including amplification of 3q26/28 and 11q13/22. A subgroup of oral cavity tumours with favourable clinical outcomes displayed infrequent copy number alterations in conjunction with activating mutations of HRAS or PIK3CA, coupled with inactivating mutations of CASP8, NOTCH1 and TP53. Other distinct subgroups contained loss-of-function alterations of the chromatin modifier NSD1, WNT pathway genes AJUBA and FAT1, and activation of oxidative stress factor NFE2L2, mainly in laryngeal tumours. Therapeutic candidate alterations were identified in most HNSCCs.