Hydropower offers highly flexible, low-carbon generation that can be used to balance electricity grids with high levels of wind and solar penetration. This will become increasingly important as the energy transition unfolds. However, hydropower generation faces several problems when used in a flexible, fast manner (on the order of seconds) when in part-load, overload, or transient conditions. Some of these issues may be addressed by an improved understanding of how the load is measured and controlled in a hydro-turbine governing system (HTGS). This paper reviews different subsystem models and stability analysis approaches for HTGS along with their applicability in different operational conditions and design layouts. The review revealed three main challenges facing the increasing flexible use of HTGS on the grid: 1) the combination of the HTGS and shaft model, 2) the control methods of HTGS with intermittent renewable energies, and 3) the uncertain nature of load on the overall performance and stability of the hydropower system. This review can stimulate further research on HTGS models and control methods to improve grid management. •Different subsystem models and stability analysis approaches for HTGS are reviewed.•Different control methods and applicability in different conditions are analyzed.