Due to the rapid development of wireless communications together with the inflexibility of the current spectrum allocation policy, radio spectrum becomes more and more exhausted. One of the critical challenges of wireless communication systems is to efficiently utilize the limited frequency resources to be able to support the growing demand of high data rate wireless services. As a promising solution, cognitive radios have been suggested to deal with the scarcity and under-utilization of radio spectrum. The basic idea behind cognitive radios is to allow unlicensed users, also called secondary users (SUs), to access the licensed spectrum of primary users (PUs) which improves spectrum utilization. In order to not degrade the performance of the primary networks, SUs have to deploy interference control, interference mitigating, or interference avoidance techniques to minimize the interference incurred at the PUs. Cognitive radio networks (CRNs) have stimulated a variety of studies on improving spectrum utilization. In this context, this thesis has two main objectives. Firstly, it investigates the performance of single hop CRNs with spectrum sharing and opportunistic spectrum access. Secondly, the thesis analyzes the performance improvements of two hop cognitive radio networks when incorporating advanced radio transmission techniques. The thesis is divided into three parts consisting of an introduction part and two research parts based on peer-reviewed publications. Fundamental background on radio propagation channels, cognitive radios, and advanced radio transmission techniques are discussed in the introduction. In the first research part, the performance of single hop CRNs is analyzed. Specifically, underlay spectrum access using M/G/1/K queueing approaches is presented in Part I-A while dynamic spectrum access with prioritized traffics is studied in Part I-B. In the second research part, the performance benefits of integrating advanced radio transmission techniques into cognitive cooperative radio networks (CCRNs) are investigated. In particular, opportunistic spectrum access for amplify-and-forward CCRNs is presented in Part II-A where collaborative spectrum sensing is deployed among the SUs to enhance the accuracy of spectrum sensing. In Part II-B, the effect of channel estimation error and feedback delay on the outage probability and symbol error rate (SER) of multiple-input multiple-output CCRNs is investigated. In Part II-C, adaptive modulation and coding is employed for decode-and-forward CCRNs to improve the spectrum efficiency and to avoid buffer overflow at the relay. Finally, a hybrid interweave-underlay spectrum access scheme for a CCRN is proposed in Part II-D. In this work, the dynamic spectrum access of the PUs and SUs is modeled as a Markov chain which then is utilized to evaluate the outage probability, SER, and outage capacity of the CCRN.