Flexible electronic devices have received great attention in the fields of foldable electronic devices, wearable electronic devices, displays, actuators, synaptic bionics and so on. Among them, high-performance flexible memory for information storage and processing is an important part. Due to its simple structure and non-volatile characteristics, flexible resistive random access memory (RRAM) is the most likely flexible memory to achieve full commercialization. At present, the minimum bending radius of flexible RRAM can reach 2 mm and the maximum ON/OFF ratio (storage window) can reach 108. However, there are some defects in reliability and durability. In the bending process, the cracks are the main cause of device failure. The charge trap sites provided by appropriate doping or the use of amorphous nanostructures can make the conductive filaments of flexible RRAM steadier. Flexible electrodes with high conductivity and flexible dielectric with stable storage properties are the main development directions of flexible RRAM materials in the future.