Vortex light fields have attracted much attention, due to their nature of optical orbital angular momentum (OAM). The unique physical characteristics of OAM endow the vortex beam with an infinite degree of freedom in high-dimensional space, and at the same time, it also brings the unusual properties of interference, diffraction and transmission to the light field. OAM identification and detection technologies are critical to development of vortex beam from fundamental research towards practical applications. The paper focused on the geometric coordinate transformation of vortex beam, as one of important research directions in the domain of OAM detection, and reviewed the technology in detail in terms of its principles, features, research progresses and applications. Geometric coordinate transformation of vortex beam refered to transforming the whole geometric structure of vortex beam by a specialized modulation phase design, which could sort and detect OAM of vortex beam easily. Compared with traditional sorting and detecting technologies, the geometric coordinate transformation technology was favored with the advantages of passive device, no energy loss, compact structure and low cost. This unique method had become an efficient and powerful tool for the spatial separation and demultiplexing of vortex beams, and had provided a new platform for advanced applications such as classical or quantum density measurement, OAM multiplier and divider, classical optical communication and quantum entanglement, showing great potentials and broad development prospect.