Rather than a black swan, the Covid-19 pandemic was more similar to a ‘grey rhino’, an event that could be (and had been) anticipated, and the effects of which could have been effectively tackled with better data sharing, stronger global health governance, adequate financial resources and a clear commitment to solidarity across the world. How is the global community taking action to ensure that Covid-19 will be the last pandemic? What other risks must be taken into account when considering future scenarios for global health security governance? What role can be imagined for the United Nations, the World Health Organization, and multi-stakeholder platforms such as COVAX? Several proposals have been advanced in the context of the G7, the G20 and through the work of several expert groups on future pandemic preparedness. The PERISCOPE project has explored in-depth the lessons learnt from the pandemic for future governance arrangements, and aims to formulate recommendations for the global, EU and national handling of future health security threats.