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Communication theory applied to lightwave channels is ordinarily carried out using the semiclassical theory of photodetection. Recent development of nonclassical light sources-whose photodetection statistics require the use of quantum theory-plus increasing interest in optics-based approaches to quantum information processing necessitates a thorough understanding of the similarities and distinctions between the semiclassical and quantum theories of optical communications. This paper is addressed to that need, focusing, for convenience, on the free-space communication channel using Gaussian states of light. The quantum version of the Huygens-Fresnel diffraction integral is reviewed, along with the semiclassical and quantum theories of direct, homodyne, and heterodyne detection. Maximally entangled Gaussian state light is used, in conjunction with quantum photodetection theory, to explain the nonclassical effects seen in Hong-Ou-Mandel interferometry and violation of the Clauser-Horne-Shimony-Holt form of Bell's inequality. The classical information capacities of several bosonic channels are reviewed, and shown to exceed what can be achieved using conventional optical receivers.