Highlights
•Socio-ecological system dynamics of the Anthropocene require novel modelling approaches.
•Models need to capture emergent properties, regime shifts and feedbacks between system components.
•Human decision making and responses are essential components of Anthropocene models.
•Modelling challenges and possible ways forward are presented.
The ‘Anthropocene’ concept provides a conceptual framework that encapsulates the current global situation in which society has an ever-greater dominating influence on Earth System functioning. Simulation models used to understand earth system dynamics provide early warning, scenario analysis and evaluation of environmental management and policies. This paper aims to assess the extent to which current models represent the Anthropocene and suggest ways forward. Current models do not fully reflect the typical characteristics of the Anthropocene, such as societal influences and interactions with natural processes, feedbacks and system dynamics, tele-connections, tipping points, thresholds and regime shifts. Based on an analysis of current model representations of Anthropocene dynamics, we identify ways to enhance the role of modeling tools to better help us understand Anthropocene dynamics and address sustainability issues arising from them. To explore sustainable futures (‘safe and operating spaces’), social processes and anthropogenic drivers of biophysical processes must be incorporated, to allow for a spectrum of potential impacts and responses at different societal levels. In this context, model development can play a major role in reconciling the different epistemologies of the disciplines that need to collaborate to capture changes in the functioning of socio-ecological systems. Feedbacks between system functioning and underlying endogenous drivers should be represented, rather than assuming the drivers to be exogenous to the modelled system or stationary in time and space. While global scale assessments are important, the global scale dynamics need to be connected to local realities and vice versa. The diversity of stakeholders and potential questions requires a diversification of models, avoiding the convergence towards single models that are able to answer a wide range of questions, but without sufficient specificity. The novel concept of the Anthropocene can help to develop innovative model representations and model architectures that are better suited to assist in designing sustainable solutions targeted at the users of the models and model results.