Benefiting from the low cost and high abundance of potassium resources, K-based batteries have attracted numerous research interest as a more sustainable battery chemist, particularly when considering the enormous demand for sustainable energy storage while limiting Li sources for Li-based batteries. However, the much larger size of the K-ion usually leads to the serious electrodes' volumetric expansion with rapid capacity fading, making the pursuit of electrodes for potassium storage with high capacity and high stability a significant challenge. The polymer electrode materials have been considered promising materials to address these issues due to their porous characteristics, insolubility in electrolytes, and flexible structural design at a molecular level. In this review, we outline the recent advancements in redox-active polymer electrodes, including anode and cathode, materials for K-based batteries, including crystalline porous coordination polymers, crystalline covalent organic polymers, amorphous polymers, and polymer composites. We discuss the electrode designs, electrochemical performances, and K-ion storage mechanism, with a focus on their structure-function correlations. With this knowledge, we propose the perspectives and challenges in designing advanced polymer electrode materials for K-based batteries. We expect this review will shed light on the further development of reliable polymer electrode materials. (c) 2025 Science Press and Dalian Institute of Chemical Physics, Chinese Academy of Sciences. Published by Elsevier B.V. and Science Press. All rights are reserved, including those for text and data mining, AI training, and similar technologies.