Although microscopic measurements, such as, Li-NMR and µ + SR, provide fundamental information on Li-diffusion in solids, it is highly preferable to combine such information with the macroscopic properties in order to obtain a new insight to improve electrochemical properties of the whole battery system and/or to develop new electrode and electrolyte materials. In fact, the comparison between a diffusion coefficient of Li (D Li ) with ionic conductivity provided the number density of mobile Li ions, i.e. carrier density in a garnet-type electrolyte material, Li 5+x La 3 Zr x Nb 1−x O 12 . Furthermore, when D Li obtained by µ + SR is compared with D Li estimated by electrochemical measurements, a reactive surface of the cathode used for the electrochemical measurements was firstly derived as a function of the Li content (x) in the cathode material, Li x (Co 1/3 Ni 1/3 Mn 1/3 )O 2 . Finally, I will make an outlook towards future developments by means of a ultra-slow muon microscope.