In electrochemistry, the important physical constants are ionic conductivity, viscosity and ion diffusion constants. Although the ionic conductivity (sigma) and viscosity (eta) have been widely obtained, measurements of diffusion constant (D) became recently possible by the pulsed field gradient (PFG) NMR method. The relations between D and eta and D and sigma are described by the Stokes-Einstein and Nernst-Einstein equations, respectively. The research and development of the Li-ion battery (LIB) is one of the most popular subjects and the observation of ion diffusion constants by the PFG-NMR methods became a state-of-the-art technique. In this chapter, PFG-NMR measurements of the diffusion constants of Li+, and the related anions and solvents of solution electrolytes and Li+, cations and anions in ionic liquids, as well as Li+ diffusion phenomena in inorganic solid electrolytes will be described.