Well-known academic and non-academic institutions call for a new approach in economics able to capture features of modern economies including, but not limited to, complexity, non-equilibrium and uncertainty. In this paper, we provide a systematic review of ecological macroeconomic models that are suitable for the investigation of low-carbon energy transitions and assess them based on the features considered desirable for a new approach in economics. We draw two main conclusions: firstly, the knowledge base and structure of these existing ecological macroeconomic models are relevant, alongside other types of models, for the creation of a new approach in economics. Secondly, the reviewed models are policy relevant, especially in the context of the complexity and urgency of rapid energy transitions, where increasingly policymakers require economic models able to capture real-world characteristics. However, further improvements are needed to these models and future research should focus on i) assuring comparability of models' results and their policy insights, ii) incorporation of the relationships between macroeconomics, finance and sustainability and iii) the institutionalization of a new approach in economics.