Solid-state batteries (SSBs) using a solid electrolyte show potential for providing improved safety as well as higher energy and power density compared with conventional Li-ion batteries. However, two critical bottlenecks remain: the development of solid electrolytes with ionic conductivities comparable to or higher than those of conventional liquid electrolytes and the creation of stable interfaces between SSB components, including the active material, solid electrolyte and conductive additives. Although the first goal has been achieved in several solid ionic conductors, the high impedance at various solid/solid interfaces remains a challenge. Recently, computational models based on ab initio calculations have successfully predicted the stability of solid electrolytes in various systems. In addition, a large amount of experimental data has been accumulated for different interfaces in SSBs. In this Review, we summarize the experimental findings for various classes of solid electrolytes and relate them to computational predictions, with the aim of providing a deeper understanding of the interfacial reactions and insight for the future design and engineering of interfaces in SSBs. We find that, in general, the electrochemical stability and interfacial reaction products can be captured with a small set of chemical and physical principles. The reliable operation of solid-state batteries requires stable or passivating interfaces between solid components. In this Review, we discuss models for interfacial reactions and relate the predictions to experimental findings, aiming to provide a deeper understanding of interface stability.