The mitochondrial genome comprises a circular, histone-free 'chromosome' of 16.6 kb of DNA, present in one or more copies in every mitochondrion. This chromosome has been tightly conserved for more than half a billion years, coding in every multicellular animal so far investigated, both vertebrate and invertebrate: (i) the same 13 protein subunits required for oxidative phosphorylation; (ii) a component of each of the two mitochondrial ribosome subunits; and (iii) the 22 transport RNAs present within the mitochondrion. Exons on the circle are tightly packed, with no spacing introns. Mitochondrial DNA is histone-free, has limited repair ability, and has a relatively high mutation-fixation rate. Inheritance is cytoplasmic and maternal, with epidemiological evidence (namely the familial distribution of polymorphisms) indicating that recombination with mtDNA of paternal origin is exceedingly rare. Thus the maintenance and evolution of mtDNA (its remarkably successful symbiotic persistence with the nuclear genome) has been essentially asexual. The machinery for homologous recombination is present in mitochondria of at least some species, however, and it might be surprising if it did not occur between circles in some circumstances. By bringing together the fields of mitochondrial biochemistry, evolutionary genetics, reproductive physiology, and neuromuscular medicine in focusing on the inheritance of normal and abnormal human mtDNA, we can hope to better understand the forces behind this genome's inheritance and what might be required of ovarian function to satisfy its accurate persistence over millions of years. Clinically we can hope also for a better understanding of ooplasmic factors in human fertility and in the wide manifestations of mitochondrial genomic disease.