The accumulation of somatic mutations in a genome is the result of the activity of one or more mutagenic processes, each of which leaves its own imprint. The study of these DNA fingerprints, termed mutational signatures, holds important potential for furthering our understanding of the causes and evolution of cancer, and can provide insights of relevance for cancer prevention and treatment. In this review, we focus our attention on the mathematical models and computational techniques that have driven recent advances in the field.