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Cognitive radio is an exciting emerging technology that has the potential of dealing with the stringent requirement and scarcity of the radio spectrum. Such revolutionary and transforming technology represents a paradigm shift in the design of wireless systems, as it will allow the agile and efficient utilization of the radio spectrum by offering distributed terminals or radio cells the ability of radio sensing, self-adaptation, and dynamic spectrum sharing. Cooperative communications and networking is another new communication technology paradigm that allows distributed terminals in a wireless network to collaborate through some distributed transmission or signal processing so as to realize a new form of space diversity to combat the detrimental effects of fading channels. In this paper, we consider the application of these technologies to spectrum sensing and spectrum sharing. One of the most important challenges for cognitive radio systems is to identify the presence of primary (licensed) users over a wide range of spectrum at a particular time and specific geographic location. We consider the use of cooperative spectrum sensing in cognitive radio systems to enhance the reliability of detecting primary users. We shall describe spectrum sensing for cognitive radios and propose robust cooperative spectrum sensing techniques for a practical framework employing cognitive radios. We also investigate cooperative communications for spectrum sharing in a cognitive wireless relay network. To exploit the maximum spectrum opportunities, we present a cognitive space-time-frequency coding technique that can opportunistically adjust its coding structure by adapting itself to the dynamic spectrum environment.