The membrane separator is a key component in a liquid-electrolyte battery for electrically separating the cathode and the anode, meanwhile ensuring ionic transport between them. Besides these basic requirements, endowing the separator with specific beneficial functions is now being paid great attention because it provides an important alternative approach for the development of batteries, particularly next-generation high-energy rechargeable batteries. Herein, functional separators are overviewed based on four key criteria of next-generation high-energy rechargeable batteries: stable, safe, smart and sustainable (4S). That is, the applied membrane materials and the corresponding functioning mechanisms of the 4S separators are reviewed. Functional separators with selective permeability have been applied to retard unwanted migration of the specific species (e.g. polysulfide anions in Li-S batteries) from one electrode to the other in order to achieve stable cycling operation. The covered battery types are Li-S, room-temperature Na-S, Li-organic, organic redox-flow (RF) and Li-air batteries. Safe, smart and sustainable separators are then described in sequence following the first criterion of stable cycling. In the final section, key challenges and potential opportunities in the development of 4S separators are discussed.