This report is the slideset used for an EU project cluster discussion witrh the European Commission in September 2025. Drawing on work from six Horizon Europe projects (ESM2025, ClimTip, TipESM, OptimESM, nextGEMS and RESCUE) this Climate and Earth System Insights briefing summarises the latest evidence on how human emissions are changing the climate and what this means for mitigation and risk management. It explores: A. How can we track progress in the real world and anticipate risks? B. How effectively will our actions result in a peak and decline in global warming? C. How stable are global climate processes and what are the global and regional impacts of climatic instability? D. Research gaps.