All-solid-state-batteries (ASSBs) are one of the most promising post-lithium-ion technologies that can increase the specific energy density and safety of secondary lithium batteries. Solid sulfide electrolytes are considered as promising candidates to be used in ASSBs owing to high ionic conductivities. In particular, solid electrolytes in the Li2S − P2S5 binary system have attracted considerable attention as they are composed of low-cost elements and they provide ionic conductivity values comparable to those of liquid electrolytes (>10−4 Scm−1). In this review, the structural properties and synthesis methods of materials in the binary system are summarized. Distinctions in local structures and Li-ion conduction properties between glassy, glass-ceramic, and crystalline materials are highlighted. Possible mechanisms are proposed for the fast ionic conduction observed in glass-ceramics. Important parameters of each synthesis method are suggested and the relationships between structure, synthesis and material properties are discussed. The goals of this review are to provide greater understanding of the state-of-the-art in the field, and to point out the overlooked aspects for application.