Many conserved eukaryotic traits, including apoptosis, two sexes, speciation and ageing, can be causally linked to a bioenergetic requirement for mitochondrial genes. Mitochondrial genes encode proteins involved in cell respiration, which interact closely with proteins encoded by nuclear genes. Functional respiration requires the coadaptation of mitochondrial and nuclear genes, despite divergent tempi and modes of evolution. Free-radical signals emerge directly from the biophysics of mosaic respiratory chains encoded by two genomes prone to mismatch, with apoptosis being the default penalty for compromised respiration. Selection for genomic matching is facilitated by two sexes, and optimizes fitness, adaptability and fertility in youth. Mismatches cause infertility, low fitness, hybrid breakdown, and potentially speciation. The dynamics of selection for mitonuclear function optimize fitness over generations, but the same selective processes also operate within generations, driving ageing and age-related diseases. This coherent view of eukaryotic energetics offers striking insights into infertility and age-related diseases.