Currently, all-solid-state lithium metal batteries are considered among the most promising energy storage devices, due to their safety and high energy density. Solid-state electrolytes, the key components of the batteries, are attracting increasing attention. This review presents an analysis of important recent advances in the field of lithium conducting solid-state electrolytes, including the mechanisms of conductivity, the main approaches to increase the conductivity, optimization of interfaces and ways to improve the stability for the main types of electrolytes, <i>i.e.</i>, inorganic, polymer and composite materials. For solid inorganic electrolytes, high conductivity and stability have been achieved; however, the problems related the formation of dense thin films and formation of a reliable contact with electrode materials are still unsolved. Polymer electrolytes are characterized by lower conductivity, which is improved upon plasticization with aprotic solvents. Composite electrolytes, for which it is possible to achieve a combination of high conductivity and good mechanical properties along with stability, are considered as the most promising. The main problems in the field of solid electrolytes for all-solid-state lithium metal batteries and possible ways to solve them are outlined.<Br>The bibliography includes 661 references.<Br> Key words: solid-state lithium battery, inorganic electrolyte, polymer electrolyte, composite electrolyte, ionic conductivity, lithium conductivity, transference numbers