Three-dimensional (3D) shape measurement technique using structured light has garnered widespread attentions and applications in traditional manufacturing industries due to its high precision and non-contact advantages. With the rapid development of emerging fields such as smart manufacturing and artificial intelligence, there is a growing demand for efficiently acquiring high-precision 3D data sources. Phase error compensation technique, as a crucial step in achieving high-precision measuring result using structured light, plays a pivotal role in improving the accuracy and efficiency of the measuring system. In this context, this paper provides a brief introduction to the principles of phase shifting profilometry and the various forms of phase errors caused by different error sources. Then, it categorizes and discusses such methods for compensating different types of errors, optimization directions, and suitable scenarios. Finally, the paper concludes by summarizing the challenges and potential development trends of phase error compensation technique based on phase-shifting fringe analysis.