Cooperative communication has the potential of providing better throughput and reliability to wireless systems when compared with direct communication. To realise the potential gain, it is important to design cooperative strategies for some representative scenarios. This survey deals with three basic wireless relay channels, namely, the parallel relay channel, the multiple‐access relay channel and the broadcast relay channel. For the first channel, which models a single unicast connection, various forwarding strategies are studied. For the second and third channels, which model, respectively, the uplink and downlink scenarios with multiple unicast connections; network codes that exploit the possibility of coding among the connections are studied. The common aim pertaining to the studies of all these three channels is to use the limited radio resource in the most efficient way. Beside the aforementioned conventional works, studies that have state‐of‐the‐art assumptions for relay networks, including outdated channel state information at the transmitter, full duplex relay and practical rateless‐coded cooperation, are also extensively reviewed. Copyright © 2014 John Wiley & Sons, Ltd.