This case study investigated students' conceptual knowledge of limits in calculus by implementing semi-structured interviews. The constructivist learning principles of Piaget and Inhelder as well as theories of understanding by Skemp guided the study. In Phase I, a pilot study was conducted with 15 students from a Calculus III class. By using 41 traditional textbook type tasks and non-traditional tasks, various ways students think about functions, limits at a point, limits at infinity and limits that do not exist were explored. Tasks included continuous and non-continuous functions; piecewise, rational and trigonometric functions, including those with oscillatory end behaviors. In Phase I, two students with different conceptions of limits and ability levels were selected for the initial analysis. The findings gave rise to a more in-depth follow-up investigation referred to as Phase II , which explored what students know about limits with respect to the definition of limit and infinity as well as knowledge of domains. Four student cases were selected out of nine based on similar emerging themes of understandings. The results are interpreted in terms of the constructivist framework and suggest that students assimilate information about limits into a variety of unique conceptual knowledge structures that ultimately develop into operational schemas. Given the nature of the content knowledge, these schemas are either appropriate or altered. Implications related to improving instructional practices, differentiating instruction for diverse learners and teaching limits in meaningful ways across the curriculum, are discussed. [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.]