This paper outlines an integrated approach to trust and relevance with respect to arguments: in particular, it is suggested that trust in relevance has a central role in argumentation. We first distinguish two types of argumentative relevance: internal relevance, i.e. the extent to which a premise has a bearing on its purported conclusion, and external relevance, i.e. a measure of how much a whole argument is pertinent to the matter under discussion, in the broader dialogical context where it is proposed. (...) Then, we argue that judgements of internal relevance heavily rely on trust, and that such trust, although occasionally misplaced , is nonetheless based on several reasons, and thus often justified, by either epistemic or pragmatic considerations. We conclude by sketching potential methods to formally model trust in argumentative relevance, and briefly discussing the technological implications of this line of research. (shrink)