This chapter reviews recent proposals about how the meanings of evidentials should be captured within formal semantic theories, which attempt to model compositional meaning in a way that gives insight into possible semantic variation. The literature surveyed addresses three questions. First, how should the core meaning of evidential morphemes be characterized and what sorts of information can be inferred from their use in particular contexts and hence does not need to be specified as part of the core meaning? Second, can the way that evidentials compose with the rest of the sentence be captured using existing formal tools, or do evidentials have semantic properties that motivate additions to our semantic toolkit? Third, is there a limit to the range of possible evidential meanings? If so, how can a formal semantic theory constrain the possible meanings?