Electronic memory devices, such as memristors, charge trap memory, and floating-gate memory, have been developed over the last decade. The use of polymers in electronic memory devices enables new opportunities, including easy-to-fabricate processes, mechanical flexibility, and neuromorphic applications. This review revisits recent efforts on polymer-based electronic memory developments. The versatile contributions of polymers for emerging memory devices are classified, providing a timely overview of such unconventional functionalities with a strong emphasis on the merits of polymer utilization. Furthermore, this review discusses the opportunities and challenges of polymer-based memory devices with respect to their device performance and stability for practical applications.