We identify a set of essential recent advances in climate change research with high policy relevance, across natural and social sciences: (1) looming inevitability and implications of overshooting the 1.5°C warming limit, (2) urgent need for a rapid and managed fossil fuel phase-out, (3) challenges for scaling carbon dioxide removal, (4) uncertainties regarding the future contribution of natural carbon sinks, (5) intertwinedness of the crises of biodiversity loss and climate change, (6) compound events, (7) mountain glacier loss, (8) human immobility in the face of climate risks, (9) adaptation justice, and (10) just transitions in food systems.