Strong pulse-like ground motions have caused extensive damage to many engineering structures and are one of the main factors influencing earthquake damage in near-fault regions. Therefore, it is necessary to study near-fault velocity pulse-like ground motions to reveal the seismic failure mechanism of engineering structures in near-fault areas and to carry out seismic fortification and seismic design. The key step is the effective identification of strong pulse-like ground motions. The strong pulse-like ground motions identified in previous studies have typically been selected by subjective judgment, because the velocity-time history of the ground motion is dominated by a large pulse. The selection of pulse-like ground motions using these approaches requires a certain level of judgment. However, the classification may not be obvious for many ground motions. Numerous researchers have attempted to capture pulse-like features using different approaches, of which simple pulse models, known as semi-quantitative methods, are commonly used. However, one limitation of semi-quantitative approaches is that most do not provide a quantitative pulse-detection scheme; that is, the classification of pulse-like ground motions may not be easily reproducible. Many quantitative classification methods for pulse-like ground motions have been developed. These quantitative classifications provide electronic libraries of recorded ground motions, list statistics indicating whether a given ground motion contains a velocity pulse, and help the science and engineering communities to access these ground motions and study their effects for research or practical applications. In brief, the identification methods for strong velocity pulse-like ground motions have undergone qualitative, semi-quantitative, and quantitative development processes. Among these methods, the quantitative identification method has the advantages of repeatability and batch processing and is increasingly recognized and applied. However, there is no uniform and definite classification principle for quantitative velocity pulse recognition methods. In this paper, three types of quantitative identification methods commonly used for velocity pulses are systematically summarized and introduced in detail from the aspects of recognition conditions, basic principles, key steps, and application scope. Representatives of these three methods are recommended, including a quantitative classification method using wavelet analysis, a quantitative identification method based on energy, and an efficient algorithm based on significant velocity half-cycles. In addition, their advantages and disadvantages were analyzed. Because of the instability of the velocity pulse recording waveform, no method can achieve a pulse recognition rate of 100%. In addition, although quantitative methods have made great progress in pulse recognition, period determination, and pulse recording direction determination, they are all based on the basic principles of signal processing methods and pulse characteristics without considering the mechanism of velocity pulse generation. Thus, it is necessary to include the above mentioned three points to synthetically identify the strong ground motions of the velocity pulse and form an optimal pulse-discriminant system. Finally, the key problems affecting the further improvement of the quantitative velocity pulse recognition method are discussed, and the research emphasis for its future development is highlighted. This provides a basic reference for beginners in the field.