Aqueous AgNO3 solution, usually used as the initial chemical shift standard in 109Ag NMR, has been studied and a concentration dependence of the 109Ag chemical shift is presented. A new standard for the CP/MAS (Cross polarization/Magic angle Spinning) set-up experiment is reported. Using high resolution MAS or CP/MAS NMR techniques, a series of inorganic silver compounds have been systematically studied by solid-state 109Ag NMR spectroscopy for the first time. A wide chemical shift range of 1350 ppm was found. The CS (Chemical shift) tensors obtained from the slow MAS or static 109Ag NMR spectra have provided valuable structural information about Ag coordination, which is in good accordance with the available crystal structure data. The data presented in this thesis represent a significant addition to the available 109Ag chemical shifts and chemical shifts anisotropies. In addition, a number of silver exchanged zeolites A, X, Y, M, LTL, and ferrierite have been studied by solid-state 109Ag NMR spectroscopy in their hydrated, dehydrated and ammoniated states. Narrow single peaks were readily observed for hydrated silver-exchanged zeolite A, X and Y but 109Ag signal in dehydrated silver-exchanged zeolites was not detectable by 109Ag NMR. The 109Ag NMR spectrum of ammoniated silver exchanged Y demonstrated the existence of intrazeolite Ag(NH3)2+ species.