With the extremely high theoretical energy densities, secondary batteries including lithium-sulfur (Li-S) and sodium-sulfur (Na-S) batteries are anticipated to become the leading candidates among metal-sulfur batteries. However, the practical energy density and storage efficiency of Li/Na-sulfur batteries are significantly hindered by several issues: the low conductivity of sulfur cathodes, substantial volume changes during charge and discharge cycles, the shuttle effect caused by metal polysulfides, and uncontrollable dendrite formation on the reactive alkali metal anodes, which also heighten safety concerns. Constructing functionalized separators is considered one of the most promising strategies to overcome these challenges and enhance the performance of Li/Na-sulfur batteries. Functionalized separators offer numerous advantages such as enhanced mechanical stability, bifunctionality in suppressing the shuttle effect and dendrite growth, and minimal impact on battery energy density and volume. However, comprehensive reviews of Li/Na-sulfur functionalized separators are relatively fewer, while the related research has increased significantly. In this context, it is crucial to provide a comprehensive review of recent advances in functionalized separators for Li/Na-sulfur batteries. First, this review offers an in-depth analysis of the current issues faced by Li/Na-sulfur batteries and summarizes the requirements of separators for improving Li/Na-sulfur batteries. Subsequently, a detailed discussion is presented about the performances and applications especially in shuttle effect inhibition and dendrite growth suppression of functionalized separators in Li-S and Na-S batteries. Finally, the review addresses the challenges and potential future research directions for functionalized separators in Li/Na-sulfur batteries.