Relevance is the potential contribution of an item in a context to a goal or outcome. The goal may be epistemic or practical. Thus the main species of relevance are epistemic, practical and causal relevance. Premiss relevance is a species of epistemic relevance. A premiss is relevant to an argument’s conclusion if and only if it can be ineliminably combined in the context with other information so as to justify or refute the argument’s conclusion, provided that the other information is at least potentially accurate and its accuracy can be determined independently of the conclusion. One can combine epistemic evaluation of the components of an argument laid out on the Toulmin model with computation of defeat statuses by considering attacks on its components, attacks on those attacks, and so forth. Such methods of evaluation can be extended to complex direct arguments but not so easily to embedded indirect arguments. For the construction of arguments, something like Dewey’s method of inquiry will be generally appropriate. In some but not all cases one will be able to use established warrants.