<p>Traditional social network models focus on pairwise interactions, overlooking the complexity of group-level dynamics that shape collective human behaviour. Here we outline how the framework of higher-order social networks—using mathematical representations beyond simple graphs—can more accurately represent interactions involving multiple individuals. Drawing from empirical data including scientific collaborations and contact networks, we demonstrate how higher-order structures reveal mechanisms of group formation, social contagion, cooperation and moral behaviour that are invisible in dyadic models. By moving beyond dyads, this approach offers a transformative lens for understanding the relational architecture of human societies, opening new directions for behavioural experiments, cultural dynamics, team science and group behaviour as well as new cross-disciplinary research.</p>