This paper is a survey of error-correcting codes, with emphasis on the costs of encoders and decoders, and the relationship of these costs to various important system parameters such as speed and delay. Following an introductory overview, the remainder of this paper is divided into three sections corresponding to the three major types of channel noise: white Gaussian noise, interference, and digital errors of the sort which occur in secondary memories such as disks. Appendix A presents some of the more important facts about modern implementations of decoders for long high-rate Reed-Solomon codes, which play an important role throughout the paper. Appendix B investigates some important aspects of the tradeoffs between error correction and error detection.