Neuromorphic computing could enable the potential to break the inherent limitations of conventional von Neumann architectures, which has led to widespread research interest in developing novel neuromorphic memory devices, such as memristors and bioinspired artificial synaptic devices. Covalent organic frameworks (COFs), as crystalline porous polymers, have tailorable skeletons and pores, providing unique platforms for the interplay with photons, excitons, electrons, holes, ions, spins, and molecules. Such features encourage the rising research interest in COF materials in neuromorphic electronics. To develop high-performance COF-based neuromorphic memory devices, it is necessary to comprehensively understand materials, devices, and applications. Therefore, this Perspective focuses on discussing the use of COF materials for neuromorphic memory devices in terms of molecular design, thin-film processing, and neuromorphic applications. Finally, we provide an outlook for future directions and potential applications of COF-based neuromorphic electronics.