Social norms have been investigated across many disciplines for many years, but until recently, studies mainly provided indirect, implicit and correlational support for the role of social norms in driving behaviour. To understand how social norms, and in particular social norm change, can generate a large-scale behavioural change to deal with some of the most pressing challenges of our current societies, such as climate change and vaccine hesitancy, we discuss and review several recent advances in social norm research that enable a more precise underpinning of the role of social norms: how to identify their existence, how to establish their causal effect on behaviour and when norm change may pass tipping points. We advocate future research on social norms to study norm change through a mechanism-based approach that integrates experimental and computational methods in theory-driven, empirically calibrated agent-based models. As such, social norm research may move beyond unequivocal praising of social norms as the missing link between self-interested behaviour and observed cooperation or as the explanation for (the lack of) social tipping. It provides the toolkit to understand explicitly where, when and how social norms can be a solution to solve large-scale problems, but also to recognize their limits.