Monogamy as a social system has been both a scientific puzzle and an important sociocultural issue for decades. In this review, we examine social monogamy from a comparative perspective with a focus on our closest genetic relatives – the primates. We break down monogamy into component elements, including social relationships, mate-guarding or jealousy, emotional/affective attachment, and biparental care. Our survey of primates shows not all features are present in species classified as socially monogamous, in the same way that human monogamous relationships may not include all elements – a perspective we refer to as ‘monogamy à la carte’. Our review concludes with a survey of the neurobiological correlates of social monogamy in primates, exploring unique or common pathways for the elemental components of monogamy. This compilation points out the remarkably complex interplay among sex-steroid and neuropeptide hormones, glucocorticoids, and the reward pathway in shaping the social phenotypes associated with monogamy in primates.