Rock drilling and blasting inevitably produce blasting vibration effects and hazards. The accurate analysis and prediction of blasting vibrations and effective active control methods are thus of great practical significance. This paper summarises the achievements in the prediction and active control of blast vibration velocities over the past 40 years. In terms of predicting the peak value of the blasting vibration velocity (PPV), empirical model prediction methods are very convenient, but their prediction accuracy and effectiveness are poor. By introducing probability and statistical theory into empirical model prediction methods, the accuracy of PPV predictions can be improved. The fundamental wave superposition prediction method can comprehensively predict the vibration velocity, frequency, and duration. However, this method requires high testing accuracy for fundamental vibration waves, which requires the establishment of a regular calibration and verification mechanism for blasting vibration data acquisition devices in the blasting industry. Artificial intelligence prediction methods can significantly improve the accuracy of PPV predictions and provide new ideas for predicting blasting vibration effects under the influence of multiple factors. However, these methods are all based on massive amounts of real and effective measured data, and a substantial database of vibration testing data samples is currently lacking. Theoretical PPV prediction models and numerical simulation prediction methods have also been proposed. However, the widespread application of these methods in engineering practice is limited owing to the requirements for professional knowledge and numerical simulation technology. In terms of the active control of blasting vibration velocity, reasonable delay time determination methods for reducing the PPV are first discussed based on the superposition interference effect of vibration waveforms. However, the recommended delay time values proposed by most current methods are only suitable for protecting a single target structure. Then, a method for actively changing the delay time to regulate the frequency components of blasting vibration is discussed from the perspective of adjusting the spectral structure of blasting vibration, which can avoid the natural vibration frequency band and reduce blast vibration hazards to buildings (structures). However, this method currently remains at the theoretical level or under model experimental-scale conditions and lacks large-scale on-site application examples for verification. Finally, several key future research directions for the prediction and control of blasting vibrations are discussed.