Quasi-solid-state electrolytes (QSSEs) and electrolytes based on ionic liquids (ILs) hold promise for addressing the inherent instability and safety concerns associated with conventional organic electrolytes in lithium–sulfur batteries (LSBs). This review explores recent studies on electrolytes for LSBs, focusing on QSSEs and IL-based electrolytes. Prominent findings include the application of polymer-based QSSEs, which have shown superior ionic conductivity at room temperature. ILs have shown an effective suppression of polysulfide shuttle, such as 1-Butyl-1-methylpyrrolidinium bis(trifluoromethylsulfonyl)imide ([Pyr14][TFSI]), contributing to extending the lifespan of LSBs. Furthermore, imidazolium-based cations in ILs used in QSSE and solid-state electrolytes (SSE) have demonstrated excellent electrode compatibility, reduced interfacial resistance, and prolonged cyclability. This review presents a concise analysis of the most outstanding electrolytes reported from 2013 to 2023. Finally, the prospects in designing QSSEs and IL-containing electrolytes guide the development of new and improved LSBs, ushering in potential breakthroughs in future energy storage technologies.