Abrupt systemic changes in ecological and socio-economic systems are a regular occurrence. While there has been much attention to studying systemic changes primarily in ecology as well as in economics, the attempts to do so for coupled socio-environmental systems are rarer. This paper bridges the gap by reviewing how models can be instrumental in exploring significant, fundamental changes in such systems. The history of modelling systemic change in various disciplines contains a range of definitions and approaches. Even so, most of these efforts share some common challenges within the modelling context. We propose a framework drawing these challenges together, and use it to discuss the articles in this thematic issue on modelling systemic change in coupled social and environmental systems. The differing approaches used highlight that modelling systemic change is an area of endeavour that would benefit from greater synergies between the various disciplines concerned with systemic change.