Single-pixel imaging uses multiple pattern modulation and calculation of single-pixel measurement values to obtain the multi-dimensional light field information of the target object. Its characteristics such as dimension reduction sub-sampling, high-sensitivity detection, and spectral adaptability brought good news for non-visible band imaging, extremely weak light detection, lidar, and other fields. For a dynamic scene, multiple single-pixel measurements in a single motion frame contradict the motion of the object, causing image blur and noise problems. Aiming at the above problems, the mathematical model of single-pixel imaging and its imaging mechanism are introduced, and the development history and application status of dynamic single-pixel imaging are reviewed, especially the achievements that researchers have made in increasing the imaging frame rate and improving imaging schemes or imaging mechanisms. The current problems of dynamic single-pixel imaging are discussed, and the future development trend is considered and prospected, so as to provide a useful reference for further scientific research in this field.