Recent material developments of fast solid oxide and lithium on conductors are reviewed. Special emphasis is placed on the correlation between the composition, structure, and electrical transport properties of perovskite-type, perovskite-related, and other inorganic crystalline materials in terms of the required functional properties for practical applications, such as fuel or hydrolysis cells and batteries. The discussed materials include Sr- and Mg-doped LaGaO3, Ba2In2O5, Bi4V2O11, RE-doped CeO2, (Li,La,)TiO3, Li3La3La3Nb2O12 (M=Nb, Ta), and Na super-ionic conductor-type phosphate. Critical problems with regard to the development of practically useful devices are discussed.