What makes literary texts attractive to the reader is its ability to convey meanings through different indirect ways known as literary devices. These function as techniques adding aesthetical effects to the text. One of many devices is wordplay--a figure of speech used by people as part of their everyday communication. This research paper aims at exploring the relation between wordplay, particularly puns, and discourse. For that end, Lewis Carroll's "Alice's Adventures in Wonderland" was selected in order to explore the functions of puns in literary texts. The puns present in the text were analyzed semantically for pun classification and pragmatically, with the help of the Relevance Theory, for the function identification of puns. Adopting the qualitative methodology, this paper is a descriptive analytical study that analyzed text samples of the ninth and tenth chapters of Carroll's work with the use of discourse, semantic, and pragmatic analyses. The results showed that the functions of puns found in the two chapters were of five kinds: creating humor, showing mastery over language, provoking the reader, drawing the attention to certain phenomena, and satirizing social practices.