This article aims at clarifying the rather generic notion of global governance, by keeping its meaning as a problem from its normative usage as a project. Further, priorities should be recognized and policy issues reordered according to their relevance. The current debate easily forgets about two threats, both poisoned remnants of modernity: only nuclear weapons and climate change deserve the name of global challenges, in as much as they can hit everybody on earth and can be addressed only by universal cooperation. They challenge politics to take over an additional role, that is to become politics for the future, for the future generations’ survival under decent conditions. Because of their severity they can motivate political actors to do so in a much more compelling way than the usual array of ‘global’ concerns. There cannot be any global governance without a strategy as to how to address the two global challenges.