In order to model relevance, we use argument diagrams (graphs), argumentation schemes, profiles of dialogue, and some tools from artificial intelligence. We show how this method helps an analyst judge relevance or irrelevance of an argument in four real examples, including a criminal trial and a parliamentary debate. We contend that this method offers important lessons for a general theory of relevance for informal logic. Some problems with notions of relevance used in linguistics are pointed out. To help build a better theory of relevance, a list of ten leading characteristics of argumentative relevance is postulated.