• The multiscale interfacial issues associated with lithium sulfur batteries are clarified and summarized. • The strategies to addressing the respective interfacial issue via designing functional polymers are included. • The importance of processing methods to the structuring process of cathode interfaces is highlighted. • This review underlines the significance for applying polymers to optimize the interfaces/interphases of lithium sulfur batteries. High energy density batteries with lithium metal as the anode have been considered the most promising next-generation storage devices applied in electric vehicles, large-scale energy storage stations and so on. However, the promising high-performance has been usually blocked by challenging interface/interphase issues at different levels inside the electrochemical cell. To address the above challenges, polymer-based interface/interphase engineering with rational structure design and flexible processing methods has been proved a very effective way. In this review, we attempt to summarize and discuss the interface/interphase issues from engineering point of view, for the different parts of batteries (cathode, separator, anode). Meanwhile, the reported solutions to these issues via rational design of functional polymers and their processing are summarized accordingly. Particularly, the functional polymer-based interface engineering for addressing the polysulfide diffusion and shuttle effects, structural instability of cathode, and growth of lithium dendrites is emphasized. Furthermore, the significance of the active material microenvironment of the cathode is discussed for a more comprehensive understanding of the interface/interphase issues. Finally, the remaining challenges and perspectives to future efforts are discussed for next-generation high-energy-density batteries.