Global history stands out by its intimate relationship to the processuality of history. As they put forms and structures of ‘global integration’ centre stage, global historians have not only made statements about the direction of history the foundation of how they define their area of study; they also ascribe at least partial explanatory power to them. The chapter argues that there is a lot to gain from stronger reflection on how global historians construe historical change over time. It delves into the theory of historical processes to develop more precise questions about directionality and presents responses global histories may offer to the teleological pitfalls of global integration. It also discusses the dialectics involved in processes of global integration and offers the outlines of a global history more attuned to the (unrealised) expectations and ‘futures pasts” among historical actors and to historical uncertainties produced under the impact of global interconnection. While the directionality/teleology problem poses particular challenges for global historians, it also can help think about multiple ‘guiding scripts’ global historians may use, refine and variegate in practice.