In the context of ongoing debates about the place of knowledge and expertise in the governance of global challenges, this article seeks to promote cross-sectoral learning about the politics and pitfalls of global science advice. It begins with the intertwined histories of the Intergovernmental Panel on Climate Change (IPCC) and the global climate policy regime, before examining the politics of different ‘framings’ of the climate problem and the challenges of building and communicating scientific consensus. We then identify three important trade-offs which the IPCC has had to negotiate: global versus local; scientific disinterestedness versus policy-relevance; and consensus versus plurality. These lessons are especially timely as global institutions begin to convene knowledge to address urgent sustainable development challenges posed by anti-microbial resistance (AMR). While the IPCC experience does not provide a wholly transportable model for science advice, we show why similar trade-offs need to be addressed at an early stage by architects of advisory systems for AMR as well as other global challenges.