We review theoretical approaches for modelling the origin, persistence and change of social norms. The most comprehensive models describe the coevolution of behaviours, personal, descriptive and injunctive norms while considering influences of various authorities and accounting for cognitive processes and between-individual differences. Models show that social norms can improve individual and group well-being. Under some conditions though, deleterious norms can persist in the population through conformity, preference falsification and pluralistic ignorance. Polarization in behaviour and beliefs can be maintained, even when societal advantages of particular behaviours or belief systems over alternatives are clear. Attempts to change social norms can backfire through cognitive processes including cognitive dissonance and psychological reactance. Under some conditions social norms can change rapidly via tipping point dynamics. Norms can be highly susceptible to manipulation, and network structure influences their propagation. Future models should incorporate network structure more thoroughly, explicitly study online norms, consider cultural variations and be applied to real-world processes. This article is part of the theme issue 'Social norm change: drivers and consequences'.
Keywords: behaviour; beliefs; cultural evolution; game theory; mathematical modelling; social evolution.