As energy storage technologies move toward safer and mechanically adaptive formats, flexible solid-state batteries have become an important platform for powering next generation deformable systems. Solid polymer electrolytes (SPEs) are promising candidates for flexible solid-state batteries because their polymer-chain flexibility, film forming capability, and interfacial adaptability enable stable solid-solid electrode-electrolyte contact under low pressure or pressure free conditions. This review summarizes recent advances in SPEs for flexible solid-state batteries, covering linear polymers, topological polymer architectures, composite and multifunctional electrolytes, and representative fabrication strategies. Application oriented SPE designs are further discussed with a focus on material and device strategies for deformation adaptability, safety enhancement, and environmental adaptability. Finally, remaining challenges and future directions are outlined to guide the rational design of high performance SPEs for flexible energy storage.