Since the late 19th century, the international scene has witnessed several waves of globalization that have transformed regulation and cooperation between nations. The current wave – that economists have defined as “globalization 4.0” – is shaped by an industrial revolution that combines digital, physical and biological transformations. Digital technology has a deep structural impact on public and private goods such as health, education, transportation or energy, which changes the terms of the global condition. It disrupts both the organization of societies and the relation between individuals and globalization. Compared to previous waves of globalization, globalization 4.0 affects the international system and runs throughout the global social fabric by increasing throughout the world the level of inequalities and by triggering subsequent polarization and fragmentation. In this global context, our current modes of cooperation and regulation are facing growing issues of legitimacy and efficiency, that are not entirely new, but that are now becoming particularly acute. Those issues of legitimacy and efficiency are furthermore complicated by a shared experience of disconnection from globalization – the rise of the globalization’s so-called “left-behinds” – that could be characterized as a form of anomy at the international level. This complex challenge has not yet been fully embraced by the major institutions of global governance. There have been however responses at the sub-global level: connectivity politics, launched by China and followed by the European Union, is one illustration of the new paths that might be taken by global policy makers.