This chapter develops the analytical framework that will be applied to the subsequent case study chapters. I combine scholarship on CPE with that on Europeanisation to develop a framework that can capture the impact of ‘divergence via Europeanisation’ in Greece, Portugal, and Ireland. I develop this framework in three ways. First, I show how CPE can identify ‘obstacles to convergence’ in the European periphery. As small, late-developing economies, Greece, Portugal, and Ireland each faced institutional limits to their attempts to ‘catch up’ with the core in terms of their forms and levels of economic growth. However, such ‘institutional stickiness’ is only part of the story. I next show how by focusing on the Europeanisation of banking and finance, parallel patterns of institutional transformation in these countries can be identified. The European periphery was actually relatively successful at adapting to projects of European financial integration. However, this success led to the unanticipated emergence of fragile, crisis-prone patterns of debt-led growth. Finally, I propose an inductive, historicist multiple case study research design. This analytical framework makes it possible to explore in subsequent chapters how Greece, Portugal, and Ireland got into trouble, in part, by following the rules of European integration.