Dam and powerhouse operation sustainability is a major concern from the hydraulic engineering perspective. Powerhouse operation is one of the main sources of vibrations in the dam structure and hydropower plant; thus, the evaluation of turbine performance at different water pressures is important for determining the sustainability of the dam body. Draft tube turbines run under high pressure and suffer from connection problems, such as vibrations and pressure fluctuation. Reducing the pressure fluctuation and minimizing the principal stress caused by undesired components of water in the draft tube turbine are ongoing problems that must be resolved. Here, we conducted a comprehensive review of studies performed on dams, powerhouses, and turbine vibration, focusing on the vibration of two turbine units: Kaplan and Francis turbine units. The survey covered several aspects of dam types (e.g., rock and concrete dams), powerhouse analysis, turbine vibrations, and the relationship between dam and hydropower plant sustainability and operation. The current review covers the related research on the fluid mechanism in turbine units of hydropower plants, providing a perspective on better control of vibrations. Thus, the risks and failures can be better managed and reduced, which in turn will reduce hydropower plant operation costs and simultaneously increase the economical sustainability. Several research gaps were found, and the literature was assessed to provide more insightful details on the studies surveyed. Numerous future research directions are recommended.