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A key issue that characterizes cooperative wireless networks is the half-duplex constraint (HDC), which refers to the inability of current modems to receive and transmit data in the same frequency at the same time. This hardware limitation results in inefficient use of system resources (bandwidth loss) as it requires dedicated bandwidth allocation for relay transmissions. Methods to overcome the HDC have been studied intensively in the literature of cooperative networks in recent years, and several approaches have been proposed. In this article we highlight four different techniques which combat the HDC by using existing technology. The first approach is non-orthogonal protocols, which allow the source to be active during relay transmissions. The second approach is the overlap of several relaying transmissions in order to mimic an ideal full-duplex operation. The third solution is the two-way relay channel where two sources exchange data via the assistance of a shared relay. Finally, the fourth approach incorporates cooperation on the "network" level and uses the cognitive radio concept to enable relay transmissions during silent periods of source terminals. These techniques summarize some of the most significant HDC solutions that cover both the physical and network layers.