3D shape measurement using phase shifting profilometry (PSP) has been extensively studied by the researchers in the past few years. With the recent binary defocused method, the measurement speed of these systems have been increased significantly. Yet, measurement errors are inevitable while imaging dynamic scenes. This is mainly because PSP methods require the object to be static for a short period of time. Researchers have developed various methods to alleviate the motion-induced errors for PSP systems. This paper reviews the various state-of-the-art motion-induced error reduction methods. The various research methods are categorized into different groups and the principles behind each method was explained. We conducted experiments to compare the potential of different algorithms in compensating the motion-induced errors. A comparative discussion is also provided to serve as a reference for selection of methods under different application scenarios. Finally, further discussions are also provided to point out opportunities for future research in this field.