Medulloblastoma is a malignant childhood brain tumour comprising four discrete subgroups. To identify mutations that drive medulloblastoma we sequenced the entire genomes of 37 tumours and matched normal blood. One hundred and thirty-six genes harbouring somatic mutations in this discovery set were sequenced in an additional 56 medulloblastomas. Recurrent mutations were detected in 41 genes not yet implicated in medulloblastoma: several target distinct components of the epigenetic machinery in different disease subgroups, e.g., regulators of H3K27 and H3K4 trimethylation in subgroup-3 and 4 (e.g., KDM6A and ZMYM3), and CTNNB1-associated chromatin remodellers in WNT-subgroup tumours (e.g., SMARCA4 and CREBBP). Modelling of mutations in mouse lower rhombic lip progenitors that generate WNT-subgroup tumours, identified genes that maintain this cell lineage (DDX3X) as well as mutated genes that initiate (CDH1) or cooperate (PIK3CA) in tumourigenesis. These data provide important new insights into the pathogenesis of medulloblastoma subgroups and highlight targets for therapeutic development.