The Li-ion batteries within the consumer electronics used in our everyday life suffer from well-known deficiencies due to the prevalent use of organic liquid electrolytes: the narrow electrochemical stability windows of the organic solvents used in these electrolytes prevent the use of high-voltage cathodes, and the flammability and volatility of the solvent molecules constitute a safety hazard. Replacing the organic liquid electrolytes with inorganic solid-state electrolytes could lead to significantly safer batteries with a higher energy density. However, most known solid-state Li-ion conductors %that could be used as electrolytes are not yet suitable for application as electrolytes, since no material satisfies the stringent requirements for safety in a high-performance battery: a wide electrochemical stability window, high mechanical stability, very low electronic mobility, and fast Li-ion conduction. Searching for materials that satisfy those requirements by means of experiments is too human-labor intensive to be done on a large scale due to the time-consuming materials synthesis and experimental characterization. Computational approaches can be easily parallelized, enabling the screening of thousands of materials to find new solid-state electrolytes for Li-ion batteries. Such a computational high-throughput screening requires an automated framework and methods that are accurate enough to predict the quantities of interest but also of sufficient computational efficiency to be applied on many materials. However, known methods to predict the Li-ion conductivity in a material are either computationally too expensive to be applied on a large scale, as is the case for first-principles molecular dynamics, or are not general enough to be performed across a wide range of materials. We present a model to calculate the Li-ion diffusion coefficient and conductivity efficiently by applying physically motivated approximations to the Hamiltonian of density-functional theory. The results obtained using this "pinball model" compare well to those from accurate first-principles molecular dynamics. This agreement provides interesting insights into the dependence of the valence electronic charge density of an ionic system on the motion of Li ions and suggests that the model can be used for screening applications. After its derivation and validation, we use the pinball model in a computational high-throughput screening to find structures with promising Li-ion diffusion. These candidate solid-state electrolytes are characterized with first-principles molecular dynamics to obtain more accurate predictions of the diffusion coefficients and pathways in these materials. The pinball model, combined with the efforts to automate molecular dynamics simulations, results in a large quantity of data stored in the form of molecular dynamics trajectories, motivating a framework to analyze these in an unsupervised manner. We describe a method to investigate the diffusion mechanism in molecular dynamics simulations by performing similarity measurements between local atomic neighborhood descriptors to detect diffusive pathways and jumps of diffusing particles in an automatic and unbiased fashion. The efforts on new methods for modeling Li-ion conductors, analyzing diffusion pathways in solid-state ionic conductors, and screening for new ceramic electrolytes are summarized in the concluding chapter, which also outlines promising possibilities for future research.