The collective somatic mutations observed in a cancer are the outcome of multiple mutagenic processes that have been operative over the lifetime of a patient. Each process leaves a characteristic imprint--a mutational signature--on the cancer genome, which is defined by the type of DNA damage and DNA repair processes that result in base substitutions, insertions and deletions or structural variations. With the advent of whole-genome sequencing, researchers are identifying an increasing array of these signatures. Mutational signatures can be used as a physiological readout of the biological history of a cancer and also have potential use for discerning ongoing mutational processes from historical ones, thus possibly revealing new targets for anticancer therapies.