This chapter presents examples of the use of first principles computer simulations in the study of two families of solid electrolyte materials-namely the family of Li phosphate, phospho-nitride, and thiophosphate materials and the family of Li oxide garnet materials. The simulation work together with related experimental studies of these solid electrolytes supports the continued development of all-solid-state battery technology. where the factor of 6 comes from the three-dimensionality of the diffusion path. This analysis was used in Sec. 3.5.