A finite-fault earthquake slip model can characterize the kinematics of rupture, which is essential for earthquake mechanism studies and seismic hazard assessments. The finite-fault model of an earthquake can be inverted from a wide range of geodetic measurements and seismic recordings. The linear least squares method minimizes misfits between observations and forward modeling and is a common approach in finite-fault inversion problems. This method may not yield the most plausible finite-fault model and has four main limitations. First, total parameter spaces are challenging to explore, and non-Gaussian parameter uncertainties cannot be evaluated. Second, to improve the stability of the fault slip inversion, fault slip smoothing operators (regularization techniques) are usually applied; however, determining the strength of smoothing a fault slip distribution is subjective. Third, the fault geometry needs to be predetermined, and different fault geometry settings can result in varying inversion results. Fourth, it is difficult to account for uncertainties in forward modeling because of imprecise Earth velocity models. In contrast, Bayesian inversion determines the probability density distribution of the model parameters, providing a globally optimized solution to all model parameters and characterizing trade-offs between pairs of model parameters. Therefore, the Bayesian approach effectively overcomes the problems encountered in linear inversion. With the rapid improvement in computer technology, Bayesian inversion has become highly developed, especially in the past decade. This review reports the results of recent Bayesian finite-fault inversion studies and explains the theory and methodology of Bayesian finite-fault inversion.