In man, cells accumulate somatic mutations of mitochondrial DNA (mtDNA) as part of normal ageing. Although the overall concentration of mutant mtDNA is low in tissue as a whole, very high numbers of various mtDNA mutations develop in individual cells within the same person, which causes age-associated mitochondrial dysfunction. Some tumours contain high numbers of mtDNA mutations that are not present in healthy tissues from the same individual. The proportion of mutant mtDNA also rises in patients with progressive neurological disease due to inherited mtDNA mutations. This increase parallels the relentless clinical progression seen in these disorders. Mathematical models suggest that the same basic cellular mechanisms are responsible for the amplification of mutant mtDNA in ageing, in tumours, and in mtDNA disease. The accumulation of cells that contain high levels of mutant mtDNA may be an inevitable result of the normal mechanisms that maintain cellular concentrations of mtDNA.