This chapter looks at competition between parties. First, the chapter outlines the ways in which party systems are described and categorized, in terms of the number of parties (in other words, fragmentation) and their ideological position (polarization). The chapter then addresses the theological models that aim to explain party competition. The chapter uses the simple spatial model here which predicts that parties position themselves close to the centre of politics to appeal to the modern voter. It then looks at competition models. These models expect parties to champion issues they ‘own’. The chapter also looks at valence models which focus on competence, leadership traits and other non-party characteristics of candidates and parties. The chapter ends with a discussion of mainstream parties, looking at how they seek to respond to the rise of challenger parties.