Biological perception system has the unique advantages of high parallelism, high error tolerance, self-adaptation and low power consumption. Using neuromorphic devices to emulate biological perceptual system can effectively promote the development of brain-computer interfaces, intelligent perception, biological prosthesis and so on. Compared with other neuromorphic devices, multi-terminal neuromorphic transistors can not only realize signal transmission and training learning at the same time, but also carry out nonlinear spatio-temporal integration and collaborative regulation of multi-channel signals. However, the traditional rigid neuromorphic transistor is difficult to achieve bending deformation and close fit with the human body, which limits the application range of neuromorphic devices. Therefore, the research of flexible neuromorphic transistor with good bending characteristics has become the focus of recent research. Firstly, this review introduces the research progress of many kinds of flexible neuromorphic transistors, including device structure, working principle and basic functions. In addition, the application of the flexible neuromorphic transistor in the field of bionic perception is also introduced. Finally, this review also gives a summary and simple prospect of the above research fields.