This article examines a range of literature on argumentation in education published since 1990 and looks at four models of argumentation in depth. It begins by acknowledging that the field of argument studies and argumentation is now large and interdisciplinary. It then draws a distinction between argument (the overall phenomenon) and argumentation (the process of arguing), suggesting that it is the latter that is of most relevance to education. An informal review of literature follows, mapped on a spectrum from those deriving from logic at one end of the spectrum, to those taking a more rhetorical line at the other. The second half of the article concentrates on four main models of argumentation as applied to education: those by Toulmin; Mitchell and Riddle; Andrews; and Kaufer and Geisler. Each is seen to have a different function and to have different strengths and weaknesses as far as a model of argumentation for education is concerned. The article concludes that no new models are required at present, but that present models need to be tested through ethnographic studies of argumentation in education settings. There is also a need for more work on theories and models of visual argumentation. Finally, the power of argumentation for social and democratic operations is emphasized.