In this work materials with possible applications in all solid state Li-ion batteries are explored using computational methods within the framework of density functional theory and kinetic Monte Carlo. The density functional theory simulations use fundamental quantum mechanics along with some approximations to produce accurate models of real materials. A smaller portion of the work uses kinetic Monte Carlo to provide qualitative information about the convergence properties of transport coefficients. The materials Li2+xSnO 3 and Li2+xSnS3 are studied in the context of electrodes for Li-ion batteries. Their structures are calculated, conduction pathways for the Li-ions predicted, open cell voltages calculated, and reactivity with lithium at the surface studied. The results for these materials provided insight into existing experimental data from the literature and made predictions for open cell voltages that had not yet been measured. The materials Li 4SnS4, Li2OHCl, and Li2OHBr are studied in the context of solid state electrolytes for Li-ion batteries. The structural properties are explored for some materials by calculating Helmholtz free energies to help understand temperature dependent phases. First principles molecular dynamics are performed on some of these materials to gain insight into the mechanisms for Li-ion diffusion, which is related to the Li-ion conductivity. The molecular dynamics simulations of these materials are also used to calculate order parameters, such as time averaged site occupancies, which provide insight into temperature dependent aspects of their structure. The computations using kinetic Monte Carlo are limited to the study of the convergence properties of transport coefficients on a lattice equivalent to the Li lattice of Li 2OHCl. These Monte Carlo simulations provide critical insight on the level of statistics needed to converge the transport coefficients related to ionic conductivity. As a whole the simulations in this research provide atomistic level knowledge of real world energy storage materials.