The energy-conversion stability of hydropower is critical to satisfy the growing demand for electricity. In low-head hydropower plants, a gravitational surface vortex is easily generated, which causes irregular shock vibrations that damage turbine performance and input-flow stability. The gravitational surface vortex is a complex fluid dynamic problem with high nonlinear features. Here, we thoroughly investigate its essential hydrodynamic properties, such as Ekman layer transport, heat/mass transfer, pressure pulsation, and vortex-induced vibration, and we note some significant scientific issues as well as future research directions and opportunities. Our findings show that the turbulent Ekman layer analytical solution and vortex multi-scale modeling technology, the working condition of the vortex across the scale heat/mass transfer mechanism, the high-precision measurement technology for high-speed turbulent vortexes, and the gas–liquid–solid three-phase vortex dynamics model are the main research directions. The vortex-induced vibration transition mechanism of particle flow in complex restricted pipelines, as well as the improvement of signal processing algorithms and a better design of anti-spin/vortex elimination devices, continue to draw attention. The relevant result can offer a helpful reference for fluid-induced vibration detection and provide a technical solution for hydropower energy conversion.