Electrolytes, which are a key component in electrochemical devices, transport ions between the sulfur/carbon composite cathode and the lithium anode in lithium-sulfur batteries (LSBs). The performance of a LSB mostly depends on the electrolyte due to the dissolution of polysulfides into the electrolyte, along with the formation of a solid-electrolyte interphase. The selection of the electrolyte and its functionality during charging and discharging is intricate and involves multiple reactions and processes. The selection of the proper electrolyte, including solvents and salts, for LSBs strongly depends on its physical and chemical properties, which is heavily controlled by its molecular structure. In this review, the fundamental properties of organic electrolytes for LSBs are presented, and an attempt is made to determine the relationship between the molecular structure and the properties of common organic electrolytes, along with their effects on the LSB performance.