This paper explores the degree to which heterodox economics can contribute to the development and use of climate-economy integrated assessment models. To do so, it introduces the field of integrated assessment modeling, with a focus on the core economic methodology used by various types of models. It then summarizes some of the literature critiquing these models and how they inform policy. The paper then provides an extended classification of ways in which heterodox economics could be applied to climate-economy models and presents a number of storylines, or pathways, which could be created using insights and methods from heterodox schools. The paper concludes with an assessment of the scope for heterodox economics to answer the criticisms of climate-economy models, finding that despite not resolving all issues, the heterodoxy has a substantial role to play.