Multiple signatures of somatic mutations have been identified in cancer genomes. Exome sequences of 1,001 human cancer cell lines and 577 xenografts revealed most common mutational signatures, indicating past activity of the underlying processes, usually in appropriate cancer types. To investigate ongoing patterns of mutational-signature generation, cell lines were cultured for extended periods and subsequently DNA sequenced. Signatures of discontinued exposures, including tobacco smoke and ultraviolet light, were not generated in vitro. Signatures of normal and defective DNA repair and replication continued to be generated at roughly stable mutation rates. Signatures of APOBEC cytidine deaminase DNA-editing exhibited substantial fluctuations in mutation rate over time with episodic bursts of mutations. The initiating factors for the bursts are unclear, although retrotransposon mobilization may contribute. The examined cell lines constitute a resource of live experimental models of mutational processes, which potentially retain patterns of activity and regulation operative in primary human cancers.