In recent years, inspired by the unique operation mode of the human brain, emulation of the perception and computing functions of synapses and neurons by artificial neuromorphic devices has attracted more and more attention. So far, many researches have been reported about neuromorphic transistors (NMT), but most devices are fabricated on rigid substrates. The flexible neuromorphic transistors can not only realize signal transmission and training learning at the same time, but also carry out nonlinear spatio-temporal integration and cooperative regulation of multiple signals. It can also closely fit the soft human skin and withstand the high physiological strain of organs and tissues. More importantly, flexible neuromorphic transistors have unique advantages and application potential in detecting low amplitude signals at physiologically relevant time scales in biological environments due to their designable flexibility and excellent biocompatibility. Flexible neuromorphic transistors have been widely used in electronic skin, artificial vision system, intelligent wearable system, and other fields. At present, it is one of the most important tasks to develop low-power consumption, high-density integrated flexible neuromorphic transistors. In this paper, the research progress of NMT based on different flexible substrates is reviewed. In addition, the bright application prospect of flexible neuromorphic transistors is prospected. This review provides a reference for the development and application of flexible neuromorphic transistors in the future.