A survey is given of the most representative results on the relay channel obtained in the period 1968-2006. Several cooperative relay strategies are presented and illustrated with examples. The direct-transmission, decode-and-forward, partial decode-and-forward, and compress-and forward lower bound on the capacity of the discrete memoryless relay channel are given. The classes of relay channels for which these bounds coincide with the cut-set upper bound are treated, such as the (semi-) deterministic and degraded relay channel, and the relay channel with orthogonal components. Coding schemes for deterministic relay channels are presented. Several connections with the multiple-access channel are pointed out. The Gaussian degraded relay channel, the Gaussian relay channel with orthogonal components, and the general AWGN relay channel are analyzed. The new topic of the relay-without-delay channel is also discussed.