All-solid-state lithium batteries (ASSLBs) are receiving attention as a prospective next-generation secondary battery technology that can reduce the risk of commercial lithium-ion batteries by replacing flammable organic liquid electrolytes with non-flammable solid electrolytes. The practical application of ASSLBs requires developing robust solid electrolytes that possess ionic conductivity at room temperature on a par with that of organic liquids. These solid electrolytes must also be thermally and chemically stable, as well as compatible with electrode materials. Inorganic solid electrolytes, including oxide and sulfide-based compounds, are being studied as promising future candidates for ASSLBs due to their higher ionic conductivity and thermal stability than polymer electrolytes. Here, we present the challenges currently facing the development of oxide and sulfide-based solid electrolytes, as well as the research efforts underway aiming to resolve these challenges.