Integrated assessment models (IAMs) have emerged as key tools for building and assessing long term climate mitigation scenarios. Due to their central role in the recent IPCC assessments, and international climate policy analyses more generally, and the high uncertainties related to future projections, IAMs have been critically assessed by scholars from different fields receiving various critiques ranging from adequacy of their methods to how their results are used and communicated. Although IAMs are conceptually diverse and evolved in very different directions, they tend to be criticised under the umbrella of ‘IAMs’. Here we first briefly summarise the IAM landscape and how models differ from each other. We then proceed to discuss six prominent critiques emerging from the recent literature, reflect and respond to them in the light of IAM diversity and ongoing work and suggest ways forward. The six critiques relate to (a) representation of heterogeneous actors in the models, (b) modelling of technology diffusion and dynamics, (c) representation of capital markets, (d) energy-economy feedbacks, (e) policy scenarios, and (f) interpretation and use of model results.

Societal transitions involve multiple actors, changes in institutions, values and technologies, and interactions across multiple sectors and scales. Given this complexity, this paper takes on the view that the societal transitions research field would benefit from the further maturation and broader uptake of modelling approaches. This paper shows how modelling can enhance the understanding of and support stakeholders to steer societal transitions. It discusses the benefits modelling provides for studying large societal systems and elaborates on different ways models can be used for transitions studies. Two model applications are presented in some detail to illustrate the benefits. Then, limitations of modelling societal transitions are discussed, which leads to an agenda for future activities: (1) better cooperation in the development of dynamic models, (2) stronger interaction with other transition scholars and stakeholders, and (3) use of additional modelling approaches that we think are relevant to and largely unexplored in transitions studies