Abstract: The genome of a cancer cell carries somatic mutations that are the cumulative consequences of the DNA damage and repair processes operative during the cellular lineage between the fertilized egg and the cancer cell. Remarkably, these mutational processes are poorly characterized. Global sequencing initiatives are yielding catalogs of somatic mutations from thousands of cancers, thus providing the unique opportunity to decipher the signatures of mutational processes operative in human cancer. However, until now there have been no theoretical models describing the signatures of mutational processes operative in cancer genomes and no systematic computational approaches are available to decipher these mutational signatures. Here, by modeling mutational processes as a blind source separation problem, we introduce a computational framework that effectively addresses these questions. Our approach provides a basis for characterizing mutational signatures from cancer-derived somatic mutational catalogs, paving the way to insights into the pathogenetic mechanism underlying all cancers.