How does global capitalism – a highly unstable system that creates vast inequalities – continue to reproduce itself? Despite the burgeoning literature on financialization, large gaps remain in our understanding of the profitability and concentration of the financial sector, and of its ability to reassert itself after financial crises. This chapter develops a framework for the analysis of the political economy of global finance that centers on the claim relation between creditors and debtors. It foregrounds creation, trading, and enforcement as key stages in the life-cycle of financial claims. At each stage, the conflict between creditors and debtors takes different forms as both sides seek to manipulate the claim relationship to their advantage. However, the two sides in this tussle are not equal. We introduce the concepts of leverage power, infrastructural power and enforcement power as analytical tools to study the inequalities and hierarchies embedded in, and reproduced via, credit-debt relationships in contemporary global financial capitalism.