Although climate change has arguably become the paradigmatic global problem, its “globality” is far from trivial. The chapter distinguishes three ways of conceiving that globality—spatial scale, geopolitical reach, thematic scope—and examines the corresponding dynamics of problem construction. These have constituted climate change, respectively as a world-spanning scientific object (planetarization); a collective action problem demanding a multilateral response (internationalization); and a cross-cutting and multidimensional problem of societal transformation (desectorialization). The analysis of these dynamics combines a political sociology lens‚ which is attentive to claims-makers and governance processes, and a science and technology studies lens‚ which foregrounds scientific practices‚ knowledge infrastructures and material artefacts. The conclusion revisits the ambiguity of “globalization.” Constructing climate change as a global problem has provided political attention to the issue. And yet, each of the dynamics above also frames the problem in a specific way, providing voice and influence to specific actors and solutions.