The proliferation of wireless services and applications over the past decade has led to the rapidly increasing demand in wireless spectrum. Hence, we have been facing a critical spectrum shortage problem even though several measurements have indicated that most licensed radio spectrum is very underutilized. These facts have motivated the development of dynamic spectrum access (DSA) and cognitive radio techniques to enhance the efficiency and flexibility of spectrum utilization. In this dissertation, we investigate design, analysis, and optimization issues for joint spectrum sensing and cognitive medium access control (CMAC) protocol engineering for cognitive radio networks (CRNs). The joint spectrum sensing and CMAC design is considered under the interweave spectrum sharing paradigm and different communications settings. Our research has resulted in four major research contributions, namely, the CMAC protocol design with parallel spectrum sensing, the CMAC protocol with sequential sensing, the CMAC protocol with cooperative sensing and the asynchronous Full-Duplex cognitive MAC. We develop various analytical models for throughput performance analysis of our proposed CMAC protocol designs. Based on these analytical models, we develop different efficient algorithms to configure the CMAC protocol including channel allocation, sensing time, transmit power, contention window to maximize the total throughput of the secondary network. Furthermore, extensive numerical results are presented to gain further insights and to evaluate the performance of our CMAC protocol designs. Both the numerical and simulation results confirm that our proposed CMAC protocols can achieve efficient spectrum utilization and significant performance gains compared to existing and unoptimized designs.