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This review addresses the current state of research into active control and suppression of vortex rope in hydroturbines under off-design operating conditions. Only active control methods that can be "switched on" when required under off-design operating conditions are considered in this work. The review focuses on air addition into the flow, as well as various auxiliary fluid jets. It includes all the best practices for vortex rope suppression in numerical and experimental studies. It can be inferred from the review that a modern flow control system should be comprehensive, designed for a specific hydroturbine geometry, and obtain feedback from the flow. Injecting ~2% of air from the impeller fairing cone appears optimal for suppressing pressure pulsations without significant efficiency loss. The cost of air injection is rarely estimated, but the use of an automatic venting system can minimize overheads and potentially improve efficiencies at low gas contents. Fluid jets ranging from 3% to 12% of the main flow rate can efficiently suppress pressure pulsations, but their high energy requirements limit their use. Azimuthal perturbation of the flow appears promising as it does not require significant energy loss, but practical implementation remains challenging as one needs to accurately know the system dynamics and be capable of real-time manipulation of the flow. [ABSTRACT FROM AUTHOR]