Abstract: Establishing a unified global height datum is one of the core objectives of the international geodetic scientific community, and also a necessary infrastructure for geoscience research on a global scale and cross-border engineering applications. The international geodesy association (IAG) released the definition of international height reference system (IHRS) in 2015 and then in 2019 set out the goal of establishing the international height reference frame (IHRF). In this paper, the theory, methods and practical problems related to the IHRS and IHRF are reviewed and studied on the basis of the theoretical foundation and definition of the global height reference system. The main research contents include the determination of gravity potential $W_{\mathrm{0}}$ of the global geoid, the determination of gravity potential based on high degree gravity field model, and the determination of gravity potential based on regional gravity field modeling. Two typical investigation cases are Colorado geoid model experiment organized by IAG and the realization of IHRS in 2020 Qomolangma height survey. The results of two typical cases demonstrate that the accuracy of gravimetric geoid model can reach 1 cm (0.1 m²/s² in gravity potential) in flat areas and general mountainous areas, and it is expected to reach 2-3 cm accuracy (0.2-0.3 m²/s² in gravity potential) even in very complex mountainous areas such as Mount Qomolangma. Based on the results of two case studies, a preliminary strategy for establishing the IHRF is proposed, including layout plan of IHRF reference stations, determination methods of IHRF related gravity potential, data requirements, standards/conventions to be followed and expected accuracy. In addition, we prospect the potential contributions of optical atomic clocks and relativistic geodesy to the unification of global height datum.