This dissertation focuses on data communication over shallow, long-range underwater acoustic (UWA) channels, which are characterized by relatively long, time-varying impulse responses and acute sensitivity to Doppler effects. The latter is a result of the slow speed of sound in water, while the former is a consequence of the waveguide nature of shallow, long-range UWA channels. A succession of novel receiver algorithms are developed which recover digital information transmitted across such channels. The first considers the case of a single, fixed source transducer transmitting information to a single, fixed receive hydrophone. The second extends the first to allow nontrivial source motion, for instance, that of an autonomous undersea vehicle. The third extends the second to allow processing of data received on an array of hydrophones. The algorithms employ iterative detection. Iterative processing is creating a paradigm shift in digital communication, made possible by ever-increasing computational capabilities. There are two major components to the algorithms: an equalizer and a decoder. The main focus of this dissertation is the former which, because of the features of the UWA channel, and since the channel is not assumed known a priori at the receiver, entails adaptive resampling to correct for Doppler distortion, adaptive filtering to estimate the time-varying channel, and adaptive equalization to compensate for intersymbol interference produced by the long channel impulse responses. While decoding is performed using standard methods, its role is nonetheless crucial to the overall functioning of the algorithms. In fact, they rely on the iterative exchange of information between equalizer and decoder, and the improvement of that information with each iteration. Successful performance of the algorithms is demonstrated using data from at-sea experiments