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The NMR probe has yielded a vast array of data for the high-Tc materials, corresponding to different compounds, ionic sites, and nuclear species, as well as to a wide variety of experimental conditions. Over the twenty years, since the discovery of superconducting cuprates, ongoing analysis and discussion of cuprate NMR data have resulted in a wealth of important insights into the physics of these exotic systems. The aims of this monograph are threefold. First, it reviews NMR methodology as it has been applied to the cuprate studies. This is addressed to NMR practitioners and to physics laypersons alike. Next, it presents a review of cuprate NMR measurements and the wide variety of phenomena which they represent. The third phase is to recount the theoretical model calculations and other proposals which have been put forward to account for these data.