Transition modelling is an emerging but growing niche within the broader field of sustainability transitions research. The objective of this paper is to explore the characteristics of this niche in relation to a range of existing modelling approaches and literatures with which it shares commonalities or from which it could draw. We distil a number of key aspects we think a transitions model should be able to address, from a broadly acknowledged, empirical list of transition characteristics. We review some of the main strands in modelling of socio-technological change with regards to their ability to address these characteristics. These are: Eco-innovation literatures (energy-economy models and Integrated Assessment Models), evolutionary economics, complex systems models, computational social science simulations using agent based models, system dynamics models and socio-ecological systems models. The modelling approaches reviewed can address many of the features that differentiate sustainability transitions from other socio-economic dynamics or innovations. The most problematic features are the representation of qualitatively different system states and of the normative aspects of change. The comparison provides transition researchers with a starting point for their choice of a modelling approach, whose characteristics should correspond to the characteristics of the research question they face. A promising line of research is to develop innovative models of co-evolution of behaviours and technologies towards sustainability, involving change in the structure of the societal and technical systems.