NMR spectroscopy is one of the newer spectroscopic techniques for investigating the static, dynamic and electronic structures of molecules adsorbed onto metal catalyst surfaces. We review recent progress in the application of solid-state NMR methods to the investigation of molecules adsorbed onto metal surfaces in an electrochemical environment: in the presence of electrolyte, and at an electrified interface under external potentiostatic control. While at a very early stage of development, the NMR-electrochemistry approach has considerable potential for investigating otherwise inaccessible aspects of electrode and adsorbate structure, and should enable a comparison of results obtained from different spectroscopies, in particular from IR spectroscopy. We present a brief review of the development of the subject, followed by details of the instrumentation necessary for NMR-electrochemistry studies. We show how spin-spin relaxation can give information on surface structure and surface diffusion, how spin-lattice relaxation can give information on the presence of conduction electron spillover onto the adsorbate, and how the NMR of surface species responds to an externally applied electric field. The C-13-NMR of CO on Pt in an electrochemical environment is compared with the C-13-NMR of CO on Pt catalysts in vacuum, which are well characterized. In the case of CN on Pt, we show large spectral shifts of the resonance as the electrode potential is varied, providing an independent measurement of the effects of the electrified interface on the chemisorption bond. Spectral sensitivity is also now adequate to observe nuclei which produce even weaker signals than C-13, such as N-15. The NMR-electrochemistry method thus opens up a broad new array of possibilities for probing static structures (from T-2), surface diffusion (from the temperature dependence of T-2) as well as electronic properties of the chemisorption bond (from T-1, and from electrode potential effects) at electrochemical interfaces, and for studying reactive intermediates and poisons on high-surface-area catalysts, such as those utilized in hydrogen and organic fuel cells.