||The scarcity of bandwidth has always been the burden of high-speed wireless communication whose demand has been tremendously increasing over the years. Spectrum utilization and efficiency can be improved by making a secondary or unlicensed user to access a spectrum hole unoccupied by a primary user (PU) at the right location and the right time. This can be achieved through the use of cognitive radio (CR) which has recently been proposed as a smart technology that allows non-legitimate or unlicensed users to utilize licensed bands opportunistically. CR users are able to listen to the surrounding wireless channel, sense the vacant spectrum bands, and make use of them. In a newer behavior of CR protocols, CR users can share the spectrum with the PU by spreading their signals over a wide frequency band. This approach imposes severe constraints on the transmission power of the CR users, which should define a certain tolerance level on the interference to the PU. This thesis is mainly built upon CR technology and aims to provide new approaches for spectrum sensing and sharing. Initial efforts are put on spectrum sensing, which is one of the defining functions of CR. In this thesis, there are two main contributions corresponding to spectrum sensing. The first part deals with improving the spectrum sensing performance. We propose a method, namely, quiet-active sensing, in which CR users sense the channel in both of the quiet and active periods. We then investigate radio cooperation in order to further improve the reliability of spectrum sensing. We shall design a likelihood ratio test (LRT) based detector, which operates over a quadratic combination of local test statistics of individual CRs. In fact, the channel occupancy state can change rapidly such that the sensing mechanism may fail to keep track of the instantaneous states due to different sensing parameters. Such a situation can result in an inaccurate sensing of the spectrum occupancy. Hence, the second part looks into optimizing the parameters affecting the sensing schemes in order to improve the sensing performance. Particularly, we examine the impact of the noise power uncertainty on the performance of various detection schemes in CR networks. Besides, we consider the case where the sensing ability is not perfect which may induce interference to the primary system. We formulate a cross-layer optimization problem to design the sensing time and optimize the transmit power in order to maximize the CR throughput subject to the interference power constraint. To further enhance the spectrum efficiency, spectrum sharing is investigated and the rest of the thesis focuses on the novel paradigm of CR communications with the multiple-input/muliple-output (MIMO) design and user cooperation. The first result proposes an opportunistic spectrum sharing approach that maximizes the throughput of the cognitive system while limiting the interference to the PU. Specifically, the proposed approach is based on a user selection algorithm, along with a zero-forcing beamforming (ZFB) scheme. Furthermore, the MIMO case is investigated, where a receive antenna selection is applied. Second, we formulate a fair transmit beamforming problem that maximizes the worst CR throughput while guaranteeing certain quality-of-service (QoS) requirement at the PU in a relay-assisted CR system.