Sustainability outcomes are influenced by natural and engineered systems, as well as social institutions—rules and norms in socio-economic systems. Understanding these institutions and incorporating them into computational models can provide important insights into why systems function the way they do and how to accelerate sustainability transitions. This study compares three modeling approaches—integrated assessment modeling (IAM), engineering–economic optimization (EEO), and agent-based modeling (ABM)—to explore how they can represent institutions. The results show that omitting institutions can influence the costs of climate mitigation and miss opportunities to leverage institutional forces to speed up emissions reduction. The study highlights the importance of incorporating heterogeneous institutions in sustainability models to better understand the distributional impacts of policies and the role of social norms and beliefs in shaping behavior. The findings suggest that models should account for both formal and informal institutions, including policies, market mechanisms, and social norms, to more accurately reflect real-world sustainability challenges. The study also emphasizes the need for collaboration between sustainability modelers and social scientists to improve the representation of institutions in models. The results indicate that explicit institutional representations can significantly affect the outcomes of sustainability models, particularly in terms of cost and distributional impacts. The study calls for future research to explore how institutions evolve over time and how they interact with other factors in sustainability transitions. The findings highlight the importance of considering both formal and informal institutions in sustainability models to better understand the complex interactions that shape sustainability outcomes.Sustainability outcomes are influenced by natural and engineered systems, as well as social institutions—rules and norms in socio-economic systems. Understanding these institutions and incorporating them into computational models can provide important insights into why systems function the way they do and how to accelerate sustainability transitions. This study compares three modeling approaches—integrated assessment modeling (IAM), engineering–economic optimization (EEO), and agent-based modeling (ABM)—to explore how they can represent institutions. The results show that omitting institutions can influence the costs of climate mitigation and miss opportunities to leverage institutional forces to speed up emissions reduction. The study highlights the importance of incorporating heterogeneous institutions in sustainability models to better understand the distributional impacts of policies and the role of social norms and beliefs in shaping behavior. The findings suggest that models should account for both formal and informal institutions, including policies, market mechanisms, and social norms, to more accurately reflect real-world sustainability challenges. The study also emphasizes the need for collaboration between sustainability modelers and social scientists to improve the representation of institutions in models. The results indicate that explicit institutional representations can significantly affect the outcomes of sustainability models, particularly in terms of cost and distributional impacts. The study calls for future research to explore how institutions evolve over time and how they interact with other factors in sustainability transitions. The findings highlight the importance of considering both formal and informal institutions in sustainability models to better understand the complex interactions that shape sustainability outcomes.