In the great majority of sexual organisms, cytoplasmic genomes such as the mitochondrial genome are inherited (almost) exclusively through only one, usually the maternal, parent. This rule probably evolved to minimize the potential spread of selfish cytoplasmic genomic mutations through a species. Maternal inheritance creates an asymmetry between the sexes from which several evolutionary consequences follow. Because natural selection on mitochondria operates only in females, mitochondrial mutations may have more deleterious effects in males than in females. Strictly uniparental inheritance creates asexual mitochondrial lineages that are vulnerable to mutation accumulation (Muller's ratchet). There is evidence that over evolutionary time mitochondrial genomes have indeed accumulated slightly deleterious mutations. Mutation accumulation in animal mitochondrial genomes is probably slowed down mainly by two processes: a severe reduction in germline mitochondrial genome copy number at some point in the life cycle, enabling more effective elimination of mutations by natural selection, and occasional recombination between maternal and paternal mitochondrial genomes following paternal leakage.