The increase of atmospheric CO2, and hence climate change, is controlled by anthropogenic emissions, but also by biogeochemical processes that currently remove anthropogenic carbon dioxide from the atmosphere, helping to limit climate change. These mitigating effects may significantly reduce in a warmer climate, amplifying risk of climate change and impacts. What are the drivers of land and ocean carbon sinks? What are the origins of variability of carbon sinks and is this variability predictable? How will the carbon cycle and feedbacks operate in a warming climate and how different were they in the past? What is the potential for amplification of climate change over the 21st century via climate-carbon cycle feedbacks? How do greenhouse gases fluxes from highly vulnerable carbon reservoirs respond to changing climate? These questions are profound to the WCRP Grand Challenge on Carbon Feedbacks in the Climate System. In our session we invite contributions from modeling, observational and process studies that address these questions in ways that link to Earth System Modeling.