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Flexible non‐volatile memories have attracted tremendous attentions for data storage for future electronics application. From device perspective, the advantages of flexible memory devices include thin, lightweight, printable, foldable and stretchable. The flash memories, resistive random access memories (RRAM) and ferroelectric random access memory/ferroelectric field‐effect transistor memories (FeRAM/FeFET) are considered as promising candidates for next generation non‐volatile memory device. Here, we review the general background knowledge on device structure, working principle, materials, challenges and recent progress with the emphasis on the flexibility of above three categories of non‐volatile memories.