Rechargeable sodium-sulfur (Na-S) batteries are regarded as a promising energy storage technology due to their high energy density and low cost. High-temperature sodium-sulfur (HT Na-S) batteries with molten sodium and sulfur as cathode materials were proposed in 1966, and later successfully commercialised for utility-scale stationary energy storage. However, their high working temperature (300-350 °C) causes some detrimental problems such as high operating costs, difficulties of maintenance (corrosion), and severe safety issues. In particular, HT Na-S batteries with Na polysulfides as the final discharge product only deliver about a third of the sulfur's theoretical capacity. These drawbacks greatly limited the broader applications of HT Na-S batteries. In recent years, extensive efforts have been devoted to developing next-generation intermediate-temperature sodium-sulfur batteries (IMT Na-S, operating at 120-300 °C) and room-temperature sodium-sulfur batteries (RT Na-S) with higher capacity, lower maintenance cost and enhanced safety. Herein, we provide a comprehensive review of the latest progress on IMT Na-S and RT Na-S batteries. We elucidate the working principles, opportunities and challenges of these non-high-temperature Na-S battery systems, and summarise the advances in the battery components including cathodes, anodes, electrolytes, and other battery constituents. In particular, the applications of solid-state electrolytes in IMT Na-S and RT Na-S chemistry are emphasised. The remaining challenges and clear perspectives are outlined for the future development of novel high-performance Na-S batteries.