Abstract Mutations are the ultimate source of genetic variation. A question that has repeatedly arisen is, whether the mutation rate undergoes evolutionary change, depending on the environmental conditions, such that evolvability is enhanced. In asexual unicellular organism, elevated mutation rates arise under stressful conditions and are among the factors that facilitate, for example, the evolution of antibiotic resistance. In asexual species, all genetic loci are linked and therefore, those loci producing genetic mutations can hitchhike to high frequency with beneficial mutations at other loci. This does not occur in sexual species, where recombination quickly detaches mutator alleles from their effects. In sexual species, the mutation rate is expected to evolve to its lowest value, given by the drift limit and the cost of fidelity. Elevated mutation rates in sexual species may arise when populations under stressful conditions are composed of maladaptive individuals with difficulties allocating resources to repair and proofreading mechanisms. Key Concepts Mutations are the ultimate source of genetic variation. The model of slightly deleterious mutations holds that most mutations are deleterious, some are neutral, and very few, beneficial. Though most mutations effects seem to be detrimental, mutations are nevertheless necessary. Intraspecific variation in repair and proofreading mechanisms enable evolutionary change in the mutation rate. Drift imposes a lower limit to the evolution of the mutation rate. The need of adaptive mutations and the cost of fidelity push the value of the mutation rate upwards, while detrimental effects and the need of replication fidelity keep the value as low as possible. Adaptive elevations of the mutation rate are not expected in sexual species, independently of habitat conditions, because of the process of recombination. Recombination separates mutator alleles from their effects. Elevated mutation rates may arise in sexual species because of critical phenotypic conditions in stressed populations.