Medulloblastoma is an aggressively growing tumour, arising in the cerebellum or medulla/brain stem. It is the most common malignant brain tumour in children, and shows tremendous biological and clinical heterogeneity. Despite recent treatment advances, approximately 40\% of children experience tumour recurrence, and 30\% will die from their disease. Those who survive often have a significantly reduced quality of life. Four tumour subgroups with distinct clinical, biological and genetic profiles are currently identified. WNT tumours, showing activated wingless pathway signalling, carry a favourable prognosis under current treatment regimens. SHH tumours show hedgehog pathway activation, and have an intermediate prognosis. Group 3 and 4 tumours are molecularly less well characterized, and also present the greatest clinical challenges. The full repertoire of genetic events driving this distinction, however, remains unclear. Here we describe an integrative deep-sequencing analysis of 125 tumour-normal pairs, conducted as part of the International Cancer Genome Consortium (ICGC) PedBrain Tumor Project. Tetraploidy was identified as a frequent early event in Group 3 and 4 tumours, and a positive correlation between patient age and mutation rate was observed. Several recurrent mutations were identified, both in known medulloblastoma-related genes (CTNNB1, PTCH1, MLL2, SMARCA4) and in genes not previously linked to this tumour (DDX3X, CTDNEP1, KDM6A, TBR1), often in subgroup-specific patterns. RNA sequencing confirmed these alterations, and revealed the expression of what are, to our knowledge, the first medulloblastoma fusion genes identified. Chromatin modifiers were frequently altered across all subgroups. These findings enhance our understanding of the genomic complexity and heterogeneity underlying medulloblastoma, and provide several potential targets for new therapeutics, especially for Group 3 and 4 patients.