Gastric cancer is a leading cause of cancer deaths, but analysis of its molecular and clinical characteristics has been complicated by histological and aetiological heterogeneity. Here we describe a comprehensive molecular evaluation of 295 primary gastric adenocarcinomas as part of The Cancer Genome Atlas (TCGA) project. We propose a molecular classification dividing gastric cancer into four subtypes: tumours positive for Epstein–Barr virus, which display recurrent PIK3CA mutations, extreme DNA hypermethylation, and amplification of JAK2, CD274 (also known as PD-L1) and PDCD1LG2 (also known as PD-L2); microsatellite unstable tumours, which show elevated mutation rates, including mutations of genes encoding targetable oncogenic signalling proteins; genomically stable tumours, which are enriched for the diffuse histological variant and mutations of RHOA or fusions involving RHO-family GTPase-activating proteins; and tumours with chromosomal instability, which show marked aneuploidy and focal amplification of receptor tyrosine kinases. Identification of these subtypes provides a roadmap for patient stratification and trials of targeted therapies.