Separators have evolved from passive polymeric barriers into multifunctional components that critically govern the performance, safety, and lifetime of liquid and quasi-solid lithium rechargeable batteries. This Review provides a comprehensive analysis of separator materials and architectures spanning commercial polyolefins and their ceramic coatings, high-temperature polymers (PI, PEEK), nanofiber and bio-derived membranes, and cross-linked gel/polymer-ceramic composites for quasi-solid systems. Design principles linking pore size, porosity, tortuosity, wettability, and Li⁺ transference to ionic conductivity and rate capability are systematically discussed, alongside mechanical and thermal requirements such as puncture resistance, dimensional stability, shutdown behavior, and flame retardance. We compare major fabrication routes-including dry and wet stretching, phase inversion, electrospinning, ceramic/oxide coating, UV/thermal crosslinking, and vacuum filtration/solution casting-and relate their process windows to separator microstructure, electrochemical performance, and scalability. Separator-electrolyte-anode interactions are analyzed with emphasis on dendrite suppression, flux homogenization, and interface stabilization in lithium-metal and quasi-solid cells. Finally, market and techno-economic trends are summarized, highlighting the trade-offs between advanced functionality and roll-to-roll manufacturability, as well as emerging directions toward intelligent (advanced) separators and PFAS-free, recyclable architectures. This review outlines quantitative targets and design strategies needed to translate next-generation separator concepts into safe, high-energy, and commercially viable lithium battery technologies.