Flexible energy storage systems are imperative for emerging flexible devices that are revolutionizing our life. Lithium-ion batteries, the current main power sources, are gradually approaching their theoretical limitation in terms of energy density. Therefore, alternative battery chemistries are urgently required for next-generation flexible power sources with high energy densities, low cost, and inherent safety. Flexible lithium-sulfur (Li-S) batteries and analogous flexible alkali metal-chalcogen batteries are of paramount interest owing to their high energy densities endowed by multielectron chemistry. In this review, we summarized the recent progress of flexible Li-S and analogous batteries. A brief introduction to flexible energy storage systems and general Li-S batteries has been provided first. Progress in flexible materials for flexible Li-S batteries are reviewed subsequently, with a detailed classification of flexible sulfur cathodes as those based on carbonaceous (e.g., carbon nanotubes, graphene, and carbonized polymers) and composite (polymers and inorganics) materials and an overview of flexible lithium anodes and flexible solid-state electrolytes. Advancements in other flexible alkali metal-chalcogen batteries are then introduced. In the next part, we emphasize the importance of cell packaging and flexibility evaluation, and two special flexible battery prototypes of foldable and cable-type Li-S batteries are highlighted. In the end, existing challenges and future development of flexible Li-S and analogous alkali metal-chalcogen batteries are summarized and prospected.