Our understanding of female-male power relationships in animals has changed over time. Evolutionary biologists once thought that male mammals held clear-cut power over females. Later, species with pronounced female power over males were presented as exceptions in a landscape of strict male power. Spotted hyenas and certain primates, including bonobos and most lemurs, were examples of female dominance. These views were reinforced by the assumption that males and females competed over different resources: males over females, and females over food.But it’s not that simple, as the research of our colleagues and our own work on various primates has shown.We reviewed studies of primate species and found that power relationships between the sexes varied significantly. In our sample, only 25 species exhibited clear male power, 16 exhibited clear female power, and the remaining species (about 70%) exhibited moderate or no sex biases in power. Most primate females can compete directly with males and often overpower them. Size and strength differences between males and femalesMales don’t always have all the power even when they are much larger and stronger than females. In an earlier study, we showed that female mandrills in Gabon sometimes outrank males that are more than three times heavier than them.Gorillas are an interesting case too. Apart from the big difference between males and females in body and canine tooth size, they are also typically presented (by scientists and non-scientists) as the species with the strictest male-biased power over females among great apes. They’ve become the “male power archetype” among animals. We drew on 25 years of data about mountain gorillas in Uganda, to test if males strictly overpower females. Our findings suggest that females may leverage support from the most powerful males to gain power over other males. Or they may leverage access to themselves, and some males yield to females to acquire such access.Our findings in mandrills and gorillas contribute a new perspective on the ecology and evolution of female-male power relationships in great apes and other primates that is not solely based on size and strength. They call for future work to investigate similar long-standing assumptions regarding the evolutionary origins of intersexual relationships across species.Factors influencing power across primatesOur comparative analysis showed that intersexual power is influenced by different factors. Generally, females rely less than males on physical force and coercion in order to gain power. Female power is more likely to prevail in species that are monogamous, have little or no body size difference between adult females and males, and/or forage primarily in trees. These are conditions that give females greater control over reproduction. By contrast, male power is more likely to prevail in species where males mate with multiple females, are primarily terrestrial, and have larger bodies or greater weapons than females. Even when these conditions are met, however, there isn’t always a clear-cut bias in intersexual power of a social group or species. Male mandrills and gorillas mate with multiple females and are terrestrial. In these species males generally have more power than females, and the highest ranking individual in a group’s social hierarchy is always a male. Yet power is not clear-cut and females can overpower other males.What males and females compete forFinally, our studies suggest that females and males often compete directly over access to resources. In the comparative study across primates, we found that contests between females and males represented on average almost half of all contests in a social primate group. In the study on mountain gorillas, we found that power relationships between females and males determined priority of access to a precious food resource, and when a female overpowered a male, she always had priority over him.Altogether, these new findings suggest that:most primate societies do not have clear-cut sex-biases in powereven in species with extreme male-biases in size and strength, females can overpower malesfemales and males compete directly over similar resources. These findings refine our interpretation of intersexual relationships across animals. They caution against oversimplified views based solely on physical strength while neglecting the complexity of their social landscape. Finally, this work shows that the human profile does not really resemble other primates where there is clear male dominance or clear female dominance. Instead, humans are closer to those “intermediate” species with moderate and flexible dominance relationships. This can inform attempts to reconstruct power relationships between men and women in early humans.Elise Huchard receives funding from CNRS and the French Agence Nationale pour la Recherche (ANR). Nikos Smit does not work for, consult, own shares in or receive funding from any company or organisation that would benefit from this article, and has disclosed no relevant affiliations beyond their academic appointment.