Several human traits pose challenges to evolutionary thinking, as they are relatively prevalent but are associated with lower reproductive success through reduced fertility and/or longevity (Darwinian puzzles). Classical examples are left handedness, homosexual preference, menopause and mental disorders. The first two examples will be examined in details, and possible evolutionary explanations will be proposed. Predictions of the theoretical models will be presented, along with empirical tests. Some interesting consequences on the functioning of stratified societies will be considered, as well as the importance of female attractiveness.