Computer-based models provide decision-makers with techno-economic insights into transition pathways for decarbonising energy systems. Such models mainly focus on techno-economic aspects and do not adequately represent the social aspects of the energy transition, although there is broad consensus that these non-technical factors are important drivers and constraints. To map the current integration and identify perspectives for future research, we ask: Which model types are particularly good at integrating social aspects? What social aspects are represented in energy models? How are these social aspects integrated? We analysed publications that apply these energy models to investigate which and how models integrate social aspects within three main modelling steps: (i) storyline, scenario, and input parameter, (ii) optimisation/simulation process and (iii) model output discussion. Results show that social aspects are mainly integrated through exogenous assumptions and output discussions. We also identify models that go beyond technical potential and pure cost optimisation/simulation. All model types integrate behaviour and lifestyle; some address public acceptance, but not transformation dynamics. Only agent-based models integrate heterogeneity of actors and public ownership. We conclude that a better representation of social aspects in energy models is needed, and that there is a high potential to improve this by combining different model types and conducting interdisciplinary research.