Supporting Quality of Service (QoS) in mobile networks requires that admission control algorithms incorporate user mobility, and limit the probability that sufficient resources are unavailable when a user must handoff. In this thesis, we develop a framework for designing such admission control algorithms, and using this framework design an admission control algorithm for coarse-grained control of system QoS. We first devise a taxonomy to explore the mathematical structure and practical design tradeoffs encountered in developing admission control algorithms. We next introduce the Perfect Knowledge Admission Control Algorithm, which, while unrealizable in practice, serves as a benchmark for evaluating admission control algorithms by using knowledge of future handoff events to exactly control the admissible region. Third, we present an extensive set of simulations (including trace-driven simulations) and, identify a number of key system parameters for algorithm design, and quantify the fundamental tradeoffs in complexity and accuracy as revealed by the taxonomy. Finally, we introduce a novel coarse grained approach to admission control termed Virtual Bottleneck Cell, which is not only scalable, has low overhead, but also is able to provision QoS in "hot spots" and system bottlenecks. The approach's novelty lies in hierarchical control of the system, without requiring any mobility models or accurate predictions of the users' future locations.