Many primary tumours have low levels of molecular oxygen (hypoxia), and hypoxic tumours respond poorly to therapy. Pan-cancer molecular hallmarks of tumour hypoxia remain poorly understood, with limited comprehension of its associations with specific mutational processes, non-coding driver genes and evolutionary features. Here, as part of the ICGC/TCGA Pan-Cancer Analysis of Whole Genomes (PCAWG) Consortium, which aggregated whole genome sequencing data from 2658 cancers across 38 tumour types, we quantify hypoxia in 1188 tumours spanning...