Toulmin's model of argumentation, developed in 1958, has guided much argumentation research in education. However, argumentation theory in philosophy and cognitive science has advanced considerably since 1958. There are currently several alternative frameworks of argumentation that can be useful for both research and practice in education. These frameworks include Walton's dialogue theory and Bayesian models of everyday arguments. This article reviews and evaluates these frameworks and shows how each can be applied instructionally (e.g., through the teaching of critical questions or probability modeling) and, from a research standpoint, in evaluating the content and quality of informal arguments. It is concluded that attention to these and other contemporary argumentation frameworks can help move the study of argumentation in education forward. (Contains 3 figures, 4 tables, and 4 footnotes.)