Political globalization is a dynamic, nonlinear, global process of increasing and complicating the interdependence between all elements of the global political system. Global political processes are processes taking place in the context of the political aspect of globalization, resulting in the structural transformation of the world system of international relations and the emergence of new global political actors, an increase in the political interconnection and interdependence between them, and the creation of a global political architecture and hierarchy. This article reveals the trends in the development of global political processes, including: the formation of a new structure and architecture for the global world; the emergence of new actors in the global political system; the manifestation of two models of modernization of the countries of the global world (the western [Atlantic] and continental); the growth of instability at the global level; the inefficiency of global governance; the conflict between globalization and the national interests of states; and the growing role of the countries of the “global periphery” in world politics. Global political challenges are potential points of political bifurcation that must be prevented. If ignored, they can develop into global political problems, and if they are not resolved, will evolve into global political risks. This article presents a classification of global political challenges and examines the causes affecting their dynamics. The author describes possible scenarios for the development of the world political system depending on the reaction of society to global political challenges and the consequences of the implementation of each.