The chapter seeks to understand the significance of contemporary radical changes in world income distribution (most notably the recent rapid rise of China, India and a handful of other peripheral countries) by comparing the present with other periods of world-hegemonic transition. The empirical core of the chapter examines the interrelationship between the rise and decline of world hegemonies and changes in the global stratification of wealth (between-country inequality) from the sixteenth century to the present. The authors find that (like the contemporary period) past periods of world-hegemonic crisis and transition have been characterized by radical transformations in the global hierarchy of wealth, although there are fundamental differences in the nature/direction of change in each transition. Drawing on world-systems theories of global inequality and hegemonic cycles, the authors conduct a comparative-historical analysis of the dynamics underlying the long-term empirical patterning in the global distribution of wealth and power. They analyse the implications of their findings for the ongoing debate about whether we are in the midst of an impending ‘great convergence’ or on the verge of a major reversal of fortunes favoring the global North/West.