As more and more wireless applications/services emerge in the market, the already heavily crowded radio spectrum becomes much scarcer. Meanwhile, however,as it is reported in the recent literature, there is a large amount of radio spectrum that is under-utilized. This motivates the concept of cognitive radio wireless networks that allow the unlicensed secondary-users (SUs) to dynamically use the vacant radio spectrum which is not being used by the licensed primary-users (PUs). In this dissertation, we investigate protocol design for both the synchronous and asynchronous cognitive radio networks with emphasis on the medium access control (MAC) layer. We propose various spectrum sharing schemes, opportunistic packet scheduling schemes, and spectrum sensing schemes in the MAC and physical (PHY) layers for different types of cognitive radio networks, allowing the SUs to opportunistically utilize the licensed spectrum while confining the level of interference to the range the PUs can tolerate. First, we propose the cross-layer based multi-channel MAC protocol, which integrates the cooperative spectrum sensing at PHY layer and the interweave-based spectrum access at MAC layer, for the synchronous cognitive radio networks. Second, we propose the channel-hopping based single-transceiver MAC protocol for the hardware-constrained synchronous cognitive radio networks, under which the SUs can identify and exploit the vacant channels by dynamically switching across the licensed channels with their distinct channel-hopping sequences. Third, we propose the opportunistic multi-channel MAC protocol with the two-threshold sequential spectrum sensing algorithm for asynchronous cognitive radio networks. Fourth, by combining the interweave and underlay spectrum sharing modes, we propose the adaptive spectrum sharing scheme for code division multiple access (CDMA) based cognitive MAC in the uplink communications over the asynchronous cognitive radio networks, where the PUs may have different types of channel usage patterns. Finally, we develop a packet scheduling scheme for the PU MAC protocol in the context of time division multiple access (TDMA)-based cognitive radio wireless networks, which is designed to operate friendly towards the SUs in terms of the vacant-channel probability. We also develop various analytical models, including the Markov chain models, M=GY =1 queuing models, cross-layer optimization models, etc., to rigorously analyze the performance of our proposed MAC protocols in terms of aggregate throughput, access delay, and packet drop rate for both the saturation network case and non-saturation network case. In addition, we conducted extensive simulations to validate our analytical models and evaluate our proposed MAC protocols/schemes. Both the numerical and simulation results show that our proposed MAC protocols/schemes can significantly improve the spectrum utilization efficiency of wireless networks.