The infertility of the mule has proved a continuing challenge to scientific thought. Since the chromosomal differences between the two parental species are so great as to render normal meiosis impossible, it is postulated that all mules and hinnies are sterile. The problem now is to explain how mules and hinnies can occasionally produce spermatozoa or ova. The appearance of the mule was sufficient to persuade the ancients that both parents, not just the male, must contribute to the make-up of the offspring. The mule has also taught us that, when the number of oocytes in the ovary is reduced, the ovary becomes the time-clock that regulates the length of the oestrous cycle. A study of gonadotrophin production in horses and donkeys bearing hybrid foals has yielded fascinating results about the immunology of pregnancy. The behaviour of the sex chromosomes of female mules and hinnies has helped to confirm the Lyon hypothesis about X-chromosome inactivation. The mule has also provided spectacular proof of the doctrine of hybrid vigour, and the marked deficiency of males at birth confirms the general truth of Haldane's Law. The mule and the hinny remain man's only successful attempt at the production of a commercially viable interspecific mammalian hybrid.