The purpose and significance of blasting-induced vibration prediction are introduced, and the development courses of the prediction methods and their advantages and disadvantages, including the statistical analysis method, dynamic analysis method, and numerical simulation method based on field measurements and the hybrid vibration course prediction method, are reviewed in detail. Based on the authors achievements, two advanced prediction methods, the improved Anderson model and the nonlinear functional series model, are introduced. Moreover, the basic principles and applicable conditions of the mode-superposition response spectrum method, the transfer function method, and the time-history analysis method, as well as their predictions of structural vibrations, are summarized. Finally, the development trend of prediction of blasting-induced vibrations is described.