The paper reviews the use of grooved surfaces and sawtooth (chevron) edges to control the flow parameters of the wings, propeller blades and elements of vane propulsion systems operating in both gaseous and liquid media. Particular attention is paid to the physical mechanisms of improving the hydrodynamic, cavitation and acoustic characteristics under the influence of a grooved surface. These mechanisms are associated with a change in the flow structure in the region of the laminar-turbulent transition, the peculiarities of the occurrence of cavitation and acoustic radiation in the region of the outgoing edges. The results of the verification of computational models describing the behavior of the flow taking into account the laminar-turbulent transition, the use of which is necessary for studying flows near a grooved surface, are presented.