Somatic mutations in cancer genomes are caused by multiple mutational processes, each of which generates a characteristic mutational signature1. Here, as part of the Pan-Cancer Analysis of Whole Genomes (PCAWG) Consortium2 of the International Cancer Genome Consortium (ICGC) and The Cancer Genome Atlas (TCGA), we characterized mutational signatures using 84,729,690 somatic mutations from 4,645 whole-genome and 19,184 exome sequences that encompass most types of cancer. We identified 49 single-base-substitution, 11 doublet-base-substitution, 4 clustered-base-substitution and 17 small insertion-and-deletion signatures. The substantial size of our dataset, compared with previous analyses3-15, enabled the discovery of new signatures, the separation of overlapping signatures and the decomposition of signatures into components that may represent associated-but distinct-DNA damage, repair and/or replication mechanisms. By estimating the contribution of each signature to the mutational catalogues of individual cancer genomes, we revealed associations of signatures to exogenous or endogenous exposures, as well as to defective DNA-maintenance processes. However, many signatures are of unknown cause. This analysis provides a systematic perspective on the repertoire of mutational processes that contribute to the development of human cancer.