All-solid-state batteries (ASSBs) with solid-state electrolytes and lithium-metal anodes have been regarded as a promising battery technology to alleviate range anxiety and address safety issues due to their high energy density and high safety. Understanding the fundamental physical and chemical science of ASSBs is of great importance to battery development. To confirm and supplement experimental study, theoretical computation provides a powerful approach to probe the thermodynamic and kinetic behavior of battery materials and their interfaces, resulting in the design of better batteries. In this review, we assess recent progress in the theoretical computations of solid electrolytes and the interfaces between the electrodes and electrolytes of ASSBs. We review the role of theoretical computation in studying the following: ion transport mechanisms, grain boundaries, phase stability, chemical and electrochemical stability, mechanical properties, design strategies and high-throughput screening of inorganic solid electrolytes, mechanical stability, space-charge layers, interface buffer layers and dendrite growth at electrode/electrolyte interfaces. Finally, we provide perspectives on the shortcomings, challenges and opportunities of theoretical computation in regard to ASSBs.