This chapter provides an introduction to the concept of semi-presidentialism and establishes a framework for the study of the politics of semi-presidential regimes. In the first part of the chapter, the evolution of the concept of semi-presidentialism will be sketched, some of the main criticisms of the concept will be considered, a slight reformulation of the standard definition of the term will be proposed and a list of semi-presidential regimes will be identified. In the second part of the chapter, a framework for the comparative study of semi-presidential regimes will be outlined. In this way, then, this chapter provides the basis both for the in-depth country studies of semi-presidentialism which follow and for the conclusion which examines the comparative experience of semi-presidentialism and addresses the issue of whether or not countries should adopt a semi-presidential form of government in preference to either presidential or parliamentary forms of government.