In an era of accelerated and extensive globalisation, the world faces a number of challenges to tackle a wide range of transboundary problems that require effective collective action. These challenges come at a time of major shifts in world order, characterised by the emergence of multi-polarity, contestation over the meaning and interpretation of sovereignty, and reassessment of the contributions of state and non-state actors. In this context, transboundary threats to human health, including emerging and re-emerging infections, rising rates of chronic diseases, inadequate access to affordable and safe medicines, spreading antimicrobial resistance and the health effects of climate change, serve as exemplars of these global governance challenges.