Abstract-In order to mitigate the shortage of wireless spectrum, the appealing concepts of cooperative communication techniques and cognitive radio networks have been combined for the sake of improving the spectral efficiency and hence the overall system throughput. We mainly survey the overlay spectrum access scheme in this novel cooperative cognitive radio (CCR) network context. Therefore the interference between the Licensed Users/Primary Users (PUs) and the Unlicensed Users/Cognitive Users (CUs) can be offset by relying on some of the CUs to act as Relay Nodes (RN). More specifically, we have investigated the cooperative relaying technique in the context of the overlay spectrum access scheme aiming for allowing the PUs to transmit at a lower power and/or at a higher throughput, while at the same time enabling the CUs to communicate using the bandwidth released. Additionally, gaming techniques can be employed for negotiating between the PUs and the CUs for determining the specific fraction of relaying and active transmission time. Therefore, we will consider two main schemes in the overlay spectrum access scheme based on the CCR network, which are the frequency division based channel as well as the timedivision based channel. Moreover, we have surveyed the relevant advances concerning the game-based model of the overlay-based CR network. Specifically, both the family of non-cooperative and cooperative games as well as matching games have been reviewed. Furthermore, we will review the joint design of coding, modulation, user-cooperation and CCR techniques, which leads to significant mutual benefits for both the PUs and CUs.