As one of the few cellular traits that can be quantified across the tree of life, DNA-replication fidelity provides an excellent platform for understanding fundamental evolutionary processes. Furthermore, because mutation is the ultimate source of all genetic variation, clarifying why mutation rates vary is crucial for understanding all areas of biology. A revealing hypothesis for mutation-rate evolution is that natural selection primarily operates to improve replication fidelity, with the ultimate limits to what can be achieved set by the power of random genetic drift. This drift-barrier hypothesis is consistent with comparative measures of mutation rates, provides a simple explanation for the  of error-prone polymerases and yields a formal counter-argument to the view that selection fine-tunes gene-specific mutation rates.