Being relevant to some topic can be informally understood as making a difference or having something to contribute. Given a sequent \(\Delta \Rightarrow \Gamma \) , we can say, somewhat schematically, that a component of the sequent is relevant to the sequent when it contributes to the validity of the sequent. Different ways of making precise the idea of contributing to the validity and different understandings of the components of a sequent lead to a hierarchy of explications of relevance. I identify four key explications, called gaunt validity, perfect validity, relevant validity, and perfectibility. Each is shown to enjoy an interesting variable sharing property. Furthermore, if we begin with a standard sequent calculus for classical logic and introduce some simple constraints on the rules, the result is a fragment of classical logic that proves exactly the gauntly valid sequents.