The anthropological record indicates that approximately 85 per cent of human societies have permitted men to have more than one wife (polygynous marriage), and both empirical and evolutionary considerations suggest that large absolute differences in wealth should favour more polygynous marriages. Yet, monogamous marriage has spread across Europe, and more recently across the globe, even as absolute wealth differences have expanded. Here, we develop and explore the hypothesis that the norms and institutions that compose the modern package of monogamous marriage have been favoured by cultural evolution because of their group-beneficial effects—promoting success in inter-group competition. In suppressing intrasexual competition and reducing the size of the pool of unmarried men, normative monogamy reduces crime rates, including rape, murder, assault, robbery and fraud, as well as decreasing personal abuses. By assuaging the competition for younger brides, normative monogamy decreases (i) the spousal age gap, (ii) fertility, and (iii) gender inequality. By shifting male efforts from seeking wives to paternal investment, normative monogamy increases savings, child investment and economic productivity. By increasing the relatedness within households, normative monogamy reduces intra-household conflict, leading to lower rates of child neglect, abuse, accidental death and homicide. These predictions are tested using converging lines of evidence from across the human sciences.