The spectrum of mutations discovered in cancer genomes can be explained by the activity of a few elementary mutational processes. We present a novel probabilistic method, EMu, to infer the mutational signatures of these processes from a collection of sequenced tumors. EMu naturally incorporates the tumor-specific opportunity for different mutation types according to sequence composition. Applying EMu to breast cancer data, we derive detailed maps of the activity of each process, both genome-wide and within specific local regions of the genome. Our work provides new opportunities to study the mutational processes underlying cancer development. EMu is available at http://www.sanger.ac.uk/resources/software/emu/.