This paper represents a welcome synthesis of the results obtained by the authors over more than a decade. The reason why such an approach is perfectly justified is found in the novelty of the control techniques of decelerated swirling flows from the conical diffuser of hydraulic turbines. The results presented in this paper refer strictly to the new passive control techniques of the swirling flows instabilities. Although the results of these new techniques have been disseminated in various papers, it is difficult to outline an overview from a collection of articles. Therefore, the present paper achieves a welcome unitary synthesis, useful to specialists in the field of turbomachines hydrodynamics. The reluctance of the turbine manufacturers on active control techniques that use external/additional energy source, led us to the choice of passive control techniques review, especially the ones developed in the last years. The first part of the paper analyzes the specialized literature that includes a variety of passive solutions for mitigating self-induced instabilities of decelerated swirling flow downstream of hydraulic turbines. Such inherent instabilities manifest intensely at far from optimal operating regimes, and represent one of the challenges of modern hydraulic turbines. The mitigation of these instabilities is an open problem, so far there are no unanimously accepted technical solutions implemented on prototype turbines. The second part of the paper includes detailed investigations on axial water injection with flow-feedback, but also more recent approaches using adjustable diaphragm in the conical diffuser.