This chapter analyses Global Byzantium by situating the medieval empire of New Rome in the history of statehood’s generalisation worldwide. Arguing that statehood remains the implicit mental furniture of History at a macro-civilizational scale, and so more or less at the micro too, the chapter proposes the dual concepts of hegemony and counterpower as a critical and methodologically anti-state approach to global history. This ‘anarchist heuristic’ is explicated through the case study of New Rome’s interactions with the region of Caucasia, especially Armenian and Georgian polities, demonstrating both Byzantine and Caucasian studies’ potentials for radical interventions in the global turn.