Human actions play an increasing role in shaping the Earth’s planetary environment, from the physical climate system to biogeochemical cycles to the functioning of the land surface. To understand and predict the future evolution of the Earth system, it is thus critical to understand the planetary boundaries of the human playing field, as well as socio-economic dynamics and their interactions with climate, and the consequences for the planetary system. There is a range of urgent questions related to this topic, from the definition of planetary boundaries, the safe operating space for humanity, thresholds and critical transitions in the global socio-environmental system, and the identification of sustainable pathways for future development.

However, the current Earth system modelling landscape lacks the tools to adequately address these challenges. Either societal dynamics is tightly constrained by economic optimization paradigms (integrated assessment modelling) or presents only as prescribed scenario input in physical Earth system models. Furthermore, feedback loops between social and environmental processes are largely absent in current Earth system models.

What is needed is a more dynamic societal sphere allowing for social tipping points, major reorganizations, revolutions and collapse in conjunction with a description of the fully coupled co-evolutionary dynamics of human societies and the natural Earth system. In this special issue, we seek novel and innovative approaches that deal with modelling socio-economic phenomena in the Earth system, their dynamics, interactions, and boundaries.

We welcome contributions applying concepts and methods that include but are not limited to the following:

• Earth and social systems thermodynamics and stoichiometry (e.g., socio-industrial metabolism);
• socio-ecological systems modelling;
• conceptual, empirical, or agent-based models from the social sciences;
• adaptive and temporal networks;
• dynamical and evolutionary game theory.