Deletions and point mutations of mitochondrial DNA (mtDNA), which are characteristic of various human mitochondrial diseases, have been identified mainly in postmitotic tissues like brain, heart and skeletal muscle of healthy humans of advanced age but not in young people. An exponential increase with age was described for deletions of mtDNA. This paper reviews the molecular basis and experimental results on mutations of mtDNA in patients with mitochondrial diseases and in aged individuals. In addition new data on the exponential increase of point mutations of mtDNA, characteristic for MERRF and MELAS disease, in extraocular muscle from elderly humans are shown. Finally the 'mitochondrial hypothesis on aging' based on stochastic somatic mutations of mtDNA is presented.