Before turning to the empirical findings from Kosovo and Medellín, this chapter provides a brief theoretical background and outlines the operationalisation of the Peace System Analysis (PSA). To do so, this chapter is divided into two parts. The first part discusses the genealogy of the peace paradigm, in which six peacebuilding phases are discussed, ending with the current phase of ‘pragmatic peacebuilding’. The second part introduces the PSA, which naturally aligns with the final phase of the peacebuilding genealogy. Each of the four components of the analytical tool is then discussed in detail, forming the analytical framework for the case study chapters on Kosovo and Medellín.