Due to the advantages of good scalability, flexibility, low cost, ease of processing, 3D‐stacking capability, and large capacity for data storage, polymer‐based resistive memories have been a promising alternative or supplementary devices to conventional inorganic semiconductor‐based memory technology, and attracted significant scientific interest as a new and promising research field. In this review, we first introduced the general characteristics of the device structures and fabrication, memory effects, switching mechanisms, and effects of electrodes on memory properties associated with polymer‐based resistive memory devices. Subsequently, the research progress concerning the use of single polymers or polymer composites as active materials for resistive memory devices has been summarized and discussed. In particular, we consider a rational approach to their design and discuss how to realize the excellent memory devices and understand the memory mechanisms. Finally, the current challenges and several possible future research directions in this field have also been discussed.