Abstract: The precise determination of the gravity potential (geopotential) field is one of the foundational tasks in geodesy. With the rapid advancements in time and frequency science, a novel relativistic geodetic approach has garnered widespread attention in geodesy and geophysics. This method, grounded in the principles of general relativity, employs high-precision atomic clocks alongside advanced time and frequency transfer techniques to accurately measure both the geopotential difference and the orthometric height (OH) difference between two arbitrary stations on the ground. Notably, the global navigation satellite system (GNSS) time and frequency transfer technique, boasts advantages such as high precision, all-weather capability, flexible networking, and economic feasibility, gradually forming an intriguing research field of geopotential determination by a GNSS frequency shift approach. First, the principle of the relativistic geodetic approach is outlined, and the mathematical model conducive to centimeter-level geopotential difference measurement is analyzed. Second, the essential characteristics of both the cable connection and GNSS frequency shift approaches are summarized. Third, a focused review is conducted on the research progress of the GNSS frequency shift approach. The two typical GNSS time and frequency transfer methods, the common view and the precise point positioning methods, are investigated in detail. Representative experiments associated with these two methods are reviewed and discussed, followed by an analysis and summary of the development of the GNSS frequency shift approach. Afterward, the critical challenges that necessitate urgent resolution within this field are delineated, including but not limited to the modeling of the GNSS receiver clock offset, the error process in GNSS time and frequency transfer, and the data process for the receiver clock offset series. Considering the vital role of high-performance clocks in the GNSS frequency shift approach, a detailed overview of the development of both microwave atomic clocks and optical atomic clocks is presented. Finally, potential applications of the GNSS frequency shift approach are explored, including high-precision geopotential difference or OH difference measurement, the establishment of a unified world height datum with high accuracy, and the simultaneous measurement of three-dimensional geometric position along with their corresponding geopotential values. This paper aims to serve as a reference for further research on geopotential determination through the GNSS frequency shift approach and related studies.