We give a historic overview and critical perspective of polyandry in the context of sexual selection. Early approaches tended to obfuscate the fact that the total matings (copulations) by the two sexes is equal, neglecting female interests and that females often mate with (or receive ejaculates from) more than one male (polyandry). In recent years, we have gained much more insight into adaptive reasons for polyandry, particularly from the female perspective. However, costs and benefits of multiple mating are unlikely to be equal for males and females. These must be assessed for each partner at each potential mating between male i and female j, and will often be highly asymmetric. Interests of i and j may be in conflict, with (typically, ultimately because of primordial sex differences) i benefitting and j losing from mating, although theoretically the reverse can also obtain. Polyandry reduces the sex difference in Bateman gradients, and the probability of sexual conflict over mating by: (i) reducing the potential expected value of each mating to males in inverse proportion to the number of mates per female per clutch, and also often by (ii) increasing ejaculate costs through increased sperm allocation. It can nevertheless create conflict over fertilization and increase conflict over parental investment. The observed mean mating frequency for the population (and hence the degree of polyandry) is likely, at least in part, to reflect a resolution of sexual conflict. Immense diversity exists across and within taxa in the extent of polyandry, and views on its significance have changed radically, as we illustrate using avian polyandry as a case study. Despite recent criticisms, the contribution of the early pioneers of sexual selection, Darwin and Bateman, remains generally valid, and should not, therefore, be negated; as with much in science, pioneering advances are more often amplified and refined, rather than replaced with entirely new paradigms.