Across many taxa, males use elaborate ornaments or complex displays to attract potential mates. Such sexually selected traits are thought to signal important aspects of male 'quality'. Female mating preferences based on sexual traits are thought to have evolved because choosy females gain direct benefits that enhance their lifetime reproductive success (e.g. greater access to food) and/or indirect benefits because high-quality males contribute genes that increase offspring fitness. However, it is difficult to explain the persistence of female preferences when males only provide genetic benefits, because female preferences should erode the heritable genetic variation in fitness that sexually selected traits signal. This 'paradox of the lek' has puzzled evolutionary biologists for decades, and inspired many hypotheses to explain how heritable variation in sexually selected traits is maintained. Here, we discuss how factors that affect mitochondrial function can maintain variation in sexually selected traits despite strong female preferences. We discuss how mitochondrial function can influence the expression of sexually selected traits, and we describe empirical studies that link the expression of sexually selected traits to mitochondrial function. We explain how mothers can affect mitochondrial function in their offspring by (a) influencing their developmental environment through maternal effects and (b) choosing a mate to increase the compatibility of mitochondrial and nuclear genes (i.e. the 'mitonuclear compatibility model of sexual selection'). Finally, we discuss how incorporating mitochondrial function into models of sexual selection might help to resolve the paradox of the lek, and we suggest avenues for future research.