Global history looms large in current historiography, yet its heuristic design and political functions remain ill-reflected. My article seeks to uncover the historical origins of the assumption that the “world” has one common history and that it is feasible and desirable to write it. I analyze the epistemic infrastructure underlying this assumption and argue that global history as practiced today is predicated on a specific mode of world-making that provides its basic template: Global history both grew out of and intellectually sustains the conception of an increasingly connected world. The type of connectedness thereby implied and reinscribed was established by what I call the “world-historical process,” a cognitive framework that co-emerged with the early modern and modern European conquest of the world through expansion, discovery, commerce, and culture. The article investigates how this process-template emerged out of the crisis of universal history that could no longer integrate and reconcile the multiple pasts of the world. The format of the world-historical process was central to Enlightenment historians' assertion of the secular and scientific prestige of their craft, as much as to its ability to discern global epochs, in particular the modern and the premodern. My article traces the fortunes of this template through historicism up to present-day global history. Current global history remains structured around the growing connectedness of previously distinct parts of the planet whose pasts are transformed into relevant world history by the very process that makes them increasingly interrelated. Global history may be too much a product of the process of globalization it studies to develop epistemologically and politically tenable alternatives to “connectivity.