Evidentiality has usually been defined as the grammaticalized expression of a speaker's evidence source for a proposition, where "evidence" is conceptualized as a speaker's source-type for a particular proposition (Aikhenvald 2004). How this evidence source-type and the evidential are related has yet to be formally modeled in the formal semantics literature. In fact, defining evidence has been considered a problem not relevant to linguistics (Faller 2002). In most cases, what is meant by the term "evidence" is never even discussed. If it were the case that evidentials exhibited regular behavior, only marking those propositions learned by whichever the particular type of evidence that it is considered to express, then the semantics of evidentials would not require further discussion. Things are not this simple, however, as there are a number of cases of evidence-evidential mismatch, where an evidential is used felicitously in spite of the fact that the speaker does not possess the correct evidence source-type (Faller 2002; Krawczyk 2009, 2010). The source-type description of evidentials does not reflect the facts, and only describes the basic, typical cases. Oversimplification of the evidential signal as source-type obscures interesting facts about evidentials and evidence. The goal of this dissertation is two-fold. The first is to provide a more thorough discussion of what it means to be evidence for evidentials; the second is to illustrate how a model of evidence can capture the semantics and pragmatics of evidentials. I formalize the notion of evidence relevant to evidentials as an evidence relation, an abductive inference to the best-fit explanation given what one observes, and propose that evidentials mark those propositions that are the best-fit explanation for the speaker's observation. I use original data from Central Alaskan Yup'ik Eskimo and English, as well as data from other publications, to illustrate how the evidence relation and best-fit explanation proposal can account for both the normal and problematic cases for the source-type approach, and provide insight into the nature of evidentiality in general. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]