The development of energy‐storage devices has received increasing attention as a transformative technology to realize a low‐carbon economy and sustainable energy supply. Lithium–sulfur (Li–S) batteries are considered to be one of the most promising next‐generation energy‐storage devices due to their ultrahigh energy density. Despite the extraordinary progress in the last few years, the actual energy density of Li–S batteries is still far from satisfactory to meet the demand for practical applications. Considering the sulfur electrochemistry is highly dependent on solid‐liquid‐solid multi‐phase conversion, the electrolyte amount plays a primary role in the practical performances of Li–S cells. Therefore, a lean electrolyte volume with low electrolyte/sulfur ratio is essential for practical Li–S batteries, yet under these conditions it is highly challenging to achieve acceptable electrochemical performances regarding sulfur kinetics, discharge capacity, Coulombic efficiency, and cycling stability especially for high‐sulfur‐loading cathodes. In this Review, the impact of the electrolyte/sulfur ratio on the actual energy density and the economic cost of Li–S batteries is addressed. Challenges and recent progress are presented in terms of the sulfur electrochemical processes: the dissolution–precipitation conversion and the solid–solid multi‐phasic transition. Finally, prospects of future lean‐electrolyte Li–S battery design and engineering are discussed.