Topological phase transition materials have strong coupling between their charge, spin orbitals, and lattice structure, which makes them have good electrical and magnetic properties, leading to promising applications in the fields of memristive devices. The smaller Gibbs free energy difference between the topological phases, the stable oxygen vacancy ordered structure, and the reversible topological phase transition promote the memristive effect, which is more conducive to its application in information storage, information processing, information calculation, and other related fields. In particular, extracting the current resistance or conductance of the two-terminal memristor to convert to the weight of the synapse in the neural network can simulate the behavior of biological synapses in their structure and function. In addition, in order to improve the performance of memristors and better apply them to neuromorphic computing, methods such as ion doping, electrode selection, interface modulation, and preparation process control have been demonstrated in memristors based on topological phase transition materials. At present, it is considered an effective method to obtain a unique resistive switching behavior by improving the process of preparing functional layers, regulating the crystal phase of topological phase transition materials, and constructing interface barrier-dependent devices. In this review, we systematically expound the resistance switching mechanism, resistance switching performance regulation, and neuromorphic computing of topological phase transition memristors, and provide some suggestions for the challenges faced by the development of the next generation of non-volatile memory and brain-like neuromorphic devices based on topological phase transition materials.