The fitness of a eukaryote hinges on the coordinated function of the products of its nuclear and mitochondrial genomes in achieving oxidative phosphorylation. I propose that sexual selection plays a key role in the maintenance of mitonuclear coadaptation across generations because it enables pre-zygotic sorting for coadapted mitonuclear genotypes. At each new generation, sexual reproduction creates new combinations of nuclear and mitochondrial genes, and the potential arises for mitonuclear incompatibilities and reduced fitness. In reviewing the literature, I hypothesize that individuals (...) engaged in mate choice select partners with correct species-typical mitochondrial and nuclear genotypes as well as individuals with highly functional cellular respiration. The implication is that mate choice for compatible nuclear and mitochondrial genes can play a significant role in generating the patterns of ornamentation and preferences observed in animals. A number of testable predictions emerge from this mitonuclear compatibility hypothesis of sexual selection. Products of mitochondrial and nuclear genes co-function to enable cellular respiration, so it is critical that compatible mitochondrial and nuclear genes be matched each generation. I propose that a core function of mate choice is selection for mitochondrial and nuclear genes that create compatible and functional combinations in offspring. (shrink)