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The all-solid-state lithium-ion battery is a promising next-generation battery technology. However, the realization of all-solid-state batteries is impeded by limited understanding of solid electrolyte materials and solid electrolyte-electrode interfaces. In this review, we present an overview of recently developed computation techniques and their applications in understanding and advancing materials and interfaces in all-solid-state batteries. We review the role of ab initio molecular dynamics simulations in studying fast ion conductors and discuss the capabilities of thermodynamic calculations powered by materials databases for identifying the chemical and electrochemical stability of solid electrolyte materials and solid electrolyte-electrode interfaces. We highlight the computational studies in the design and discovery of new solid electrolyte materials and outline design guidelines for solid electrolytes and their interfaces …