Some of the existential threats we currently face are global in the sense that they affect us all, and thus matter of global concern and trigger duties of moral global solidarity. But some of these global threats, such as the COVID-19 pandemic, are global in a second, additional, sense: discharging them requires joint, coordinated global action. For that reason, these twofold global threats trigger political – not merely moral – duties of global solidarity. This article explores the contrast between these two types of global threats with the purpose of clarifying the distinction between moral and political duties of global solidarity. And, in the absence of a fully developed global democratic institutional system, the article also explores some promising ways to fulfill our global political duties, especially those based on mechanisms of collective intelligence such as CrowdLaw, which might provide effective solutions to these global threats while enhancing the democratic legitimacy of public decision-making.