Rechargeable lithium-ion, lithium-sulfur, zinc-air, and redox-flow batteries are the most anticipated multipurpose platforms for future generations of electric vehicles, consumer devices, and portable electronics because of their high-energy density and cost-effective electrochemical energy storage. Over the past decades, a variety of novel separator membranes and electrolytes have been developed to improve rechargeable battery performance while not thoroughly addressing the issue of flammability, safety, and low cycling stability of high-energy-density batteries. This comprehensive review mainly underlines the optimization and modification of porous membranes for battery separator applications, covering four significant types: microporous separators, nonwoven mat separators, polymer electrolyte membranes, and composite membrane separators. Furthermore, the present trends in material selection for batteries are reviewed, and different choices of cathode, anode, separator, and electrolyte materials are discussed, which will also serve as key components to boost the development of next-generation rechargeable batteries.