Many words can be used flexibly: a book can be physically heavy, but also have provocative content, a "chicken" might live in a coop, but could also be tasty to eat. What do the uses of "polysemous" words such as these reveal about the structure of language and thought? Paper 1 examined 4-year-old children's representations of polysemous words like "book." After being taught a novel word to refer to one of these words' meanings, children understood an extension to the other meaning, suggesting that the meanings rely on a common representational base. However, children did not extend a novel word between homophonous meanings (e.g., between "bat" [baseball] and "bat" [animal], suggesting they are represented as separate words. Paper 2 examined children's representations of the meanings of words like "chicken," which, unlike the meanings of "book," refer to different physical entities and are encountered in distinct contexts. Children understood extensions between the meanings of these words, while rejecting extensions between conceptually related meanings that are not polysemous (e.g., between "chicken" and "egg"). Children were also able to generalize polysemous relations to novel cases, predicting how the "novel" meanings of novel words can and cannot shift. This early abstract knowledge of polysemous relations could arise from experience using polysemous words, or could be independent of linguistic experience and follow directly from flexible conceptual structures. Paper 3 focused on a specific case of polysemy: the uses of words like "long" to describe both spatial length and temporal duration. Adult participants were better able to access a structural similarity between length and duration than one between length and loudness, suggesting that the uses of "long" reveal functional overlap between representations of length and duration. Nine-month-old infants showed the same pattern of results, suggesting that this functional overlap is not constructed because of learning to flexibly use words like "long," but might instead constrain children's expectations about how those words can be used. The findings of this dissertation are discussed as they bear on the representational basis of flexible language and the interaction between flexibility in language and in thought. [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.]