Whole-genome sequencing has brought the cancer genomics community into new territory. Thanks to the sheer power provided by the thousands of mutations present in each patient's cancer, we have been able to discern generic patterns of mutations, termed 'mutational signatures', that arise during tumorigenesis. These mutational signatures provide new insights into the causes of individual cancers, revealing both endogenous and exogenous factors that have influenced cancer development. This Review brings readers up to date in a field that is expanding in computational, experimental and clinical directions. We focus on recent conceptual advances, underscoring some of the caveats associated with using the mutational signature frameworks and highlighting the latest experimental insights. We conclude by bringing attention to areas that are likely to see advancements in clinical applications.