In synchrotron radiation field, the apertures of optical components increase gradually and their surface figure precisions have been demanded to be a nano-radian level. This paper researches the modern surface figure measurement methods in this field, stitching interferometry, to realize the high resolution two-dimensional measurement of optical components. The basic principles of the stitching interferometry are introduced. Then, a series of common optical surface shape measurement instruments in the synchrotron radiation field are overviewed, such as long trace profilers based on laser beams, high precision and auto-collimation measuring machines for nanometer optical components and stitching interferometers. It describes their development history and working characteristics and compares their shortcomings and advantages. Finally, this paper analyzes the main error sources involved in the stitching interferometry, and points out that the application and development trends of the technology are mainly the innovation of the stitching algorithm, the improvement of measuring speeds of interferometers, the commercialization of interferometers and the integration of the interferometry and other science technologies.