Novel sequencing technologies are making it increasingly possible to measure the mutation rates of somatic cell lineages. Accurate germline mutation rate measurement technologies have also been available for a decade, making it possible to assess how this fundamental evolutionary parameter varies across the tree of life. Here, we review some classical theories about germline and somatic mutation rate evolution that were formulated using principles of population genetics and the biology of aging and cancer. We find that somatic mutation rate measurements, while still limited in phylogenetic diversity, seem consistent with the theory that selection to preserve the soma is proportional to life span. However, germline and somatic theories make conflicting predictions regarding which species should have the most accurate DNA repair. Resolving this conflict will require carefully measuring how mutation rates scale with time and cell division and achieving a better understanding of mutation rate pleiotropy among cell types.