Now out in Nature Human Behaviour! 🚀🚀 Over the past decades, research on collective human behaviour has relied heavily on networks. This is intuitive: people interact with other people. However, we argue that this dominant framework misses a crucial ingredient. Traditional networks represent agents as nodes and pairwise relations as edges. As a result, they fundamentally assume that social interactions can be decomposed into pairs. Yet many social processes are irreducibly group-based. A simple example: a group of three coauthors writing a paper cannot be reduced to three independent pairs of coauthors. The group itself matters. In this article, we review a wide range of empirical and theoretical cases where group interactions cannot be decomposed into pairwise ones, and show that higher-order interactions shape collective behaviour above and beyond dyadic ties. We advocate studying collective behaviour on hypergraphs, where interactions can involve multiple agents simultaneously. We review how hypergraphs provide new insights across domains, including affiliation and collaboration networks, high-frequency contact settings (families, friends), and key social processes such as social contagion, cooperation, truth-telling, and moral behaviour. Finally, we outline promising directions for future research: addressing computational challenges of higher-order models; studying bias and inequality in group dynamics; combining hypergraphs and large language models to investigate the coevolution of language and behaviour; and using higher-order networks to simulate the impact of policies before implementation; and others. We are very excited about this work and hope it will inspire further research in a rapidly growing and fundamental area with broad real-world implications. Link to the paper in the first reply This work was brilliantly led by Federico Battiston (@fede7j), with an outstanding team of co-authors: Fariba Karimi (@fariba_k), Sune Lehmann, Andrea Bamberg Migliano, Onkar Sadekar (@OnkarSadekar), Angel Sanchez, & Matjaz Perc (@matjazperc)