Memristors have recently emerged as promising contenders for in-memory computing and artificial neural networks, attributed to their analogies to biological synapses and neurons in structural and electrical behaviors. From the diversity level, a variety of materials have been demonstrated to have great potential for memristor applications. Herein, we focus on one class of crystalline materials (CMs)-based flexible memristors with state-of-the-art experimental demonstrations. Firstly, the typical device structure and switching mechanisms are introduced. Secondly, the recent advances on CMs-based flexible memristors, including 2D materials, metal-organic frameworks, covalent organic frameworks, and perovskites, as well as their applications for data storage and neuromorphic devices are comprehensively summarized. Finally, the future challenges and perspectives of CMs-based flexible memristors are presented.