We discuss how different models assessing climate change integrate aspects of structural change that are crucial to improve understanding of the relation between changes in the environment and in the economy. We identify six related aspects of structural change, which have significant impact on climate change: sectoral composition, industrial organisation, technology, employment, final demand, and institutions. Economic models vary substantially with respect to the aspects of structural change that they include, and how they model them. We review different modelling families and compare these differences: integrated assessment models (IAM), computable general equilibrium (CGE) models, structural change models (SCM), ecological macroeconomics models in the Keynesian tradition (EMK) and evolutionary agent based models (EABM). We find that IAM and CGE address few of the aspects of structural change identified; SCM focus on the sectoral composition; and EKM study final demand and employment structure. But all these models are aggregate and omit the complexity of the interactions between structural and climate change. EABM have explored a larger number of aspects of structural change, modelling their emergence from the interaction of microeconomic actors, but have not yet exploited their potential to study the interactions among interrelated aspects of structural and climate change.