In cellular networks, a recent trend is to make spectrum access dynamic in the spatial and temporal dimensions, for the sake of efficient utilization of spectrum. In such a model, the spectrum is divided into channels and is periodically allocated to the base stations in both centralized and distributed manners with different goals in mind for each approach.For the centralized approach, an auction-based market mechanism is favored due to its simplicity, efficiency and high utilization of the spectrum. The model consists of a centralized spectrum broker who owns a part of the spectrum, divides it into channels and issues short-term dynamic spectrum leases of these channels to competing base stations in the region it controls. The base stations, on the other hand, bid for channels depending on their spectrum demands. Subject to wireless interference between base stations, the broker allocates channels to them with various objectives in mind. These objectives include maximizing the generated revenue, optimizing social-choice functions like the social-welfare and/or controlling the strategic behavior of the base stations. In this dissertation, we address the above problem and show how to optimize the solution for these different objectives.As for the distributed approach, the focus is shifted towards more stable allocation that can maintain certain properties with minimal cost and human intervention even when faced by frequent network topology changes. This is demonstrated by problems such as self-configuration of fractional frequency reuse (FFR) patterns for LTE/WiMAX networks.In this dissertation, we present distributed algorithms that provide the network designer a flexible tool to tune different objectives like efficiency, stability and near-optimal spectrum utilization. For each possible choice made by the system designer, our tool delivers a near-optimal spectrum utilization with specific guarantees on the rest of the desired properties.