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This paper is concerned with an examination of how statistical communication theory can be used to combat the effects of atmospheric turbulence in optical communication systems. The objective is to provide a framework to be used in discussing and relating the analytical results presently available in the literature as well as some new, or at least not widely known, results and in motivating and guiding future work. Both digital communication and parameter and waveform estimation are considered, with the greater emphasis on the former. As necessary mathematical preliminaries, the relevant statistical channel model, the problems of spatial representation, quantum field models, and the output statistics of optical detectors are considered. For digital-communication systems, the structure and performance of optimum quantum receivers and of structured receivers, e.g., direct-and heterodyne-detection receivers with either a single detector or a detector array, are discussed and related. The simplifying approximations and assumptions required to obtain these results are emphasized. Estimation theory is considered primarily from a classical (nonquantum) viewpoint. The quadratic functional structure of the processors that result from certain approximations to the likelihood functional are emphasized. Cramer-Rao bounds on the estimation performance are considered and applied to several examples.