Around the world polygynous marriage (one man, several women) is vastly more common than polyandrous marriage (one woman, several men), and women tend to be more cautious about entering into sexual relationships than men are. Such patterns are often assumed to reflect essential differences between the sexes. However, the same dichotomy between "ardent" males and "coy" females is not found in other primates. Furthermore, under a range of circumstances females enhance their reproductive success by mating with multiple partners and use polyandrous mating (soliciting copulations from several or more males) to circumvent male-imposed costs on their free choice of mates. The existence of one-male mating systems does not prove that females "naturally" gravitate to them. Typically monandrous (copulating with just one partner) mating systems are maintained by one male excluding rivals or by other circumstances that distort female options. As with many other animals, primate females (including women) can benefit reproductively from polyandrous matings. Understanding this takes us beyond narrow research programs intent on demonstrating "universal" differences between the sexes, and allows us to study females as flexible and opportunistic individuals who confront recurring reproductive dilemmas and tradeoffs within a world of shifting options.