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A fundamental goal in cancer research is to understand the mechanisms of cell transformation. This is key to developing more efficient cancer detection methods and therapeutic approaches. One milestone towards this objective is the identification of all the genes with mutations capable of driving tumours. Since the 1970s, the list of cancer genes has been growing steadily. Because cancer driver genes are under positive selection in tumorigenesis, their observed patterns of somatic mutations across tumours in a cohort deviate from those expected from neutral mutagenesis. These deviations, which constitute signals of positive selection, may be detected by carefully designed bioinformatics methods, which have become the state of the art in the identification of driver genes. A systematic approach combining several of these signals could lead to a compendium of mutational cancer genes. In this Review, we present the Integrative OncoGenomics (IntOGen) pipeline, an implementation of such an approach to obtain the compendium of mutational cancer drivers. Its application to somatic mutations of more than 28,000 tumours of 66 cancer types reveals 568 cancer genes and points towards their mechanisms of tumorigenesis. The application of this approach to the ever-growing datasets of somatic tumour mutations will support the continuous refinement of our knowledge of the genetic basis of cancer.