Since their discovery, the fullerenes have challenged scientists with a wide array of problems concerning their properties, behavior and potential applications. One such fundamental question is that of the assembly of these carbon cages. Much effort has been directed at obtaining an understanding of the process whereby graphite is transformed into fullerenes. In this work, a theoretical study is carried out to explore the nature of carbon clusters, including the fullerenes themselves as well as other structures which may be intermediates along the path to fullerenes. The experiments which generate fullerenes are interpreted by the use of theoretical calculations, and this interpretation is used to develop a model for a fullerene assembly pathway. The principal tenets of the model are as follows: (1) The process of forming fullerenes is begun by the cycloaddition of monocyclic carbon rings, (2) The cycloadducts, once formed, undergo unimolecular reactions to form cylindrical carbon "hoops", (3) Closed cages can form from "hoops" through a sequence of 1,2-carbon shifts and cyclization reactions, and (4) The cages can "anneal" to find the most stable isomer by rearranging their bonds. Energetics of the reactions involved in each step of the model will be explored computationally by the Hartree-Fock method and several electron correlation methods. Energetic details will include both overall reaction energetics and transition barriers for the reactions. The computational results will be shown to be consistent with experimental results, so that a reasonable synthesis of theory and experiment can be presented.