International commitment to the appropriately ambitious Paris climate agreement and the United Nations Sustainable Development Goals in 2015 has pulled into the limelight the urgent need for major scientific progress in understanding and modelling the Anthropocene, the tightly intertwined social-techno-ecological planetary system that humanity now inhabits. The Anthropocene qualitatively differs from previous eras in Earth’s history in three key characteristics: (1) There is planetary-scale human agency. (2) There are social and economic networks of teleconnections spanning the globe. (3) It is dominated by planetary-scale social-ecological feedbacks. Bolting together old concepts and methodologies cannot be an adequate approach to describing this new geological era. Instead, we need a new paradigm in Earth System science that is founded equally on a deep understanding of the physical and biological Earth System – and of the economic, technological, social and cultural forces that are now an intrinsic part of it. It is time to close the loop and bring socially mediated dynamics and the technosphere explicitly into theory, analysis and computer models that let us study the whole Earth System.