There are a large number of three-dimensional (3D) shape measurement requirements and applications for objects with shiny surfaces, such as ceramics, ancient artifacts, and metal workpieces. However, the traditional fringe projection method cannot accurately measure shiny surfaces due to the large range of reflectivity of the objects with shiny surfaces and the limited maximum gray level of the camera. This paper reviewed the recent developments, application fields and future research directions of high dynamic range 3D shape measurement technologies of shiny surface. First, according to the principle and measurement method, the existing 3D measurement technologies of high dynamic range were divided into the following six categories: multiple exposures methods, projected patterns intensities adjusting methods, polarizing filters methods, color invariants methods, photometric stereo technology and miscellaneous technologies. Then, the advantages and disadvantages of these technologies were compared in detail and their adaptability was summarized. Finally, this paper summarized the application fields of shiny surfaces in 3D shape measurement technology and prospects the future research directions. It can provide users with the optimal 3D measurement method according to the different application requirements and the different measurement conditions, eventually the 3D shape of shiny surfaces can be reconstructed more accurately.