Facing the era of information explosion and the advent of artificial intelligence, there is a growing demand for information technologies with huge storage capacity and efficient computer processing. However, traditional silicon-based storage and computing technology will reach their limits and cannot meet the post-Moore information storage requirements of ultrasmall size, ultrahigh density, flexibility, biocompatibility, and recyclability. As a response to these concerns, polymer-based resistive memory materials have emerged as promising candidates for next-generation information storage and neuromorphic computing applications, with the advantages of easy molecular design, volatile and non-volatile storage, flexibility, and facile fabrication. Herein, we first summarize the memory device structures, memory effects, and memory mechanisms of polymers. Then, the recent advances in polymer resistive switching materials, including single-component polymers, polymer mixtures, 2D covalent polymers, and biomacromolecules for resistive memory devices, are highlighted. Finally, the challenges and future prospects of polymer memory materials and devices are discussed. Advances in polymer-based memristors will open new avenues in the design and integration of high-performance switching devices and facilitate their application in future information technology.