The Toulmin diagram layout is very familiar and widely used, particularly in the teaching of critical thinking skills. The conventional box-and-arrow diagram is equally familiar and widespread. Translation between the two throws up a number of interesting challenges. Some of these challenges (such as the relationship between Toulmin warrants and their counterparts in traditional diagrams) represent slightly different ways of looking at old and deep theoretical questions. Others (such as how to allow Toulmin diagrams to be recursive) are diagrammatic versions of questions that have already been addressed in artificial intelligence models of argument. But there are further questions (such as the relationships between refutations, rebuttals an...