Abstract The evolution of sexes is closely tied to uniparental inheritance (UPI) of mitochondrial DNA (mtDNA), where only females transmit mtDNA. Unlike nuclear DNA, mtDNA is highly polyploid and never evolved to be part of meiotic sex. Modelling shows that UPI increases mtDNA mutational variance, enhancing selection for high-quality mtDNA and promoting the emergence of sexes from mating types in unicellular eukaryotes. Paternal control of mitochondrial transfer favours some degree of mtDNA leak