The causes, mechanisms and consequences of mate choice and competition for mates are currently among the most intensively discussed topics in evolutionary biology. However, and despite the fact that Darwin himself published on sexual selection in monkeys, primates are notably under-represented in this field. I will explore the relationship between social organization and reproductive strategies in primates. From the male perspective, the extent of competition for mates is dependent on the defensibility of females, which depends, in turn, on the distribution of resources. Where males can monopolise access to more than one female, male-male competition is intense, and males have evolved large body size, weapons (canine teeth) and displays that both impress rivals and attract females. Where more than one male mates with a receptive female, they have evolved large testes and other adaptations that improve their chances in sperm competition. However, male reproductive success is not only about the quantity of offspring sired, but also their quality, and male primates also show paternal care where this increases offspring survival and reproduction. Furthermore, copulation can be costly for males, and they also show mate choice, concentrating mating effort on females that are most likely to conceive and produce surviving offspring. Moving to the female perspective, it has become increasingly clear that female primates promote polyandrous mating where possible, confusing paternity and thus avoiding infanticide by non-sires. However, females may combine paternity confusion with choice for particular mates, via both pre- and post-copulatory mate choice. Females also compete for access to males under certain circumstances. Finally, I will show how male and female strategies bring the sexes into direct conflict over reproduction, leading to an arms race between the sexes. Mating systems in primates, as in other taxa, can thus be viewed as evolutionarily dynamic resolutions of conflicts of interest between males and females.