Potassium-ion batteries (PIBs) exhibit electrochemical properties similar to those of lithium-ion batteries (LIBs) but with higher crustal reserves of raw materials. Owing to the safety risks of volatile liquid organic electrolytes, including leakage, dendrites and flammability, solid-state electrolytes (SSEs) have emerged as promising candidates with high safety and alignment with future green energy demands. This review highlights recent progress in SSEs for solid-state potassium-ion batteries (SSPIBs), evaluates strategies to enhance ionic transport, and discusses their chemical and electrochemical stability in depth. Although the lower solvation energy and smaller Stokes radius of K+ (compared with Li+ and Na+) endow it with faster transport kinetics in some liquid electrolytes, the electrochemical performance improvement is negligible due to the non-rate-determining step of K+ transport at this stage. It is worth noting that some K-based SSEs demonstrate comparable ionic conductivity to Li and Na-based SSEs, which plays an important role in enhancing the transport kinetics in SSPIBs because of the rate-determining step at this stage. For instance, in ETPTA polymer systems, the weaker electrostatic interaction between K+ and electronegative functional groups enables superior ion transport (ionic conductivity of 5.15 × 10−3 S cm−1 and a transference number of 0.92), outperforming Na-based (3.66 × 10−3 S cm−1 and 0.64) and Li-based analogues (1.34 × 10−3 S cm−1 and 0.22). Specifically, the weak interactions associated with the large ionic radius and the excellent interfacial wettability enabled by the low melting point are summarized. Finally, challenges and future development of SSPIBs are discussed.