Earthquake dynamic inversion aims to infer the tectonic stress and friction parameters on the fault from the rupture process or observed waveforms related to an earthquake. Earthquake dynamic inversion has been developing for more than thirty years and its research methods have undergone significant changes. In this review, the history of earthquake dynamic inversion is summarized from the aspects of the friction law, the inversion strategies, the data used in the inversion, the parameterization, and the methods of spontaneous rupture simulation. Some researches are taken as examples to further illustrate the trade-offs among these aspects. The methods on earthquake dynamic inversion are classified as two strategies, one based on repeated spontaneous rupture simulation and the other based on the calculation of stress time history. In the former strategy, various inversion algorithms were introduced in 2004 to directly invert observed waveforms, while the classical trial-and-error approach has continued to be used. A large number of dynamic models are visited in this strategy, making it possible to provide an ensemble of plausible models, which can be further utilized to assess the sensitivity to individual model parameters as well as the trade-offs among them. However, inversion algorithms lead to a great number of spontaneous rupture simulations, requiring the number of model parameters to be limited and an efficient method of simulation to be employed. The latter strategy, popular in the 1990s, does not need to repeat spontaneous rupture simulations many times, allowing a computationally expensive simulation method and a general parameterization to be used. Nevertheless, with the latter strategy, one can only invert the kinematic rupture process, which may introduce bias in the dynamic parameters. In the 1990s, the slip-weakening friction law became widely used and contributed to the development of the latter strategy. The history of earthquake dynamic inversion provides vital insights. When investigating a specific earthquake, the inversion strategy as well as the parameterization and the simulation method should be carefully decided. The choice of the simulation method mainly depends on the velocity structure, the fault geometry and the computing resource available. The parameterization should be decided considering the magnitude of the earthquake as well as the resolution of the data.