Elemental sulfur, with low cost and high theoretical capacity, has attracted considerable research interest over the past decade, but its dependence on ether electrolytes with the formation of soluble polysulfides hinders its further application. The use of sulfur-equivalent materials based on covalently bonded sulfur opens a new way to develop polysulfide-free lithium-sulfur batteries through a direct solid-solid conversion pathway. They are also compatible with commercially more reliable carbonate electrolytes to replace the highly volatile ether electrolytes. As three typical types of sulfur-equivalent cathode materials, sulfurized carbons, sulfurized polymers, and metal polysulfides have emerged with great potentials to address the intrinsic issues associated with elemental sulfur cathode and enable truly high-energy-density lithium-sulfur batteries. This perspective attempts to provide insights on the structural, electrochemical reaction mechanism, and energy density analysis of these sulfur-equivalent cathode materials. Emphasis is focused on the current technical challenges of these sulfur-equivalent materials and possible solutions for their future development.