In the last decade, a new strand of energy and climate research emerged that links quantitative models and socio-technical transitions theories or frameworks. Linking the two enables capturing the co-evolution of society, technology, the economy and the environment. We systematically review this literature (N = 44) and describe the papers' trends, scope, temporal and spatial foci, and methodological strategies. The reviewed literature aspires to find solutions to the energy and climate challenges, to increase realism in models and theories, and to enable interdisciplinary learning between the two scholarly communities. The outcomes in this literature show benefits of interdisciplinary learning between modellers and transitions theorists. However, the literature rarely identified practical insights for energy and climate solutions or for improving realism in models and theories. We conclude by suggesting that integrative research should be continued, but redirected to provide more practical outcomes to meet energy and climate targets.