Location, strength and structure of tip and edge vortices shed from wings and bodies can be manipulated by using flow control techniques. Flow physics of these approaches involve flow separation from the edge, roll-up into the vortex, wing flow regime, vortex instabilities, vortex-vortex interactions, and vortex-turbulence interactions. Actuators include continuous and unsteady blowing and suction, bleed, and control surfaces, which add momentum, vorticity and turbulence into the vortices. It is noted that actuation may have effects on more than one aspect of the flow phenomena. A comparative review of the control of delta wing vortices, tip vortices, and afterbody vortices is presented. The delay of vortex breakdown and the promotion of flow reattachment require different considerations for slender and nonslender delta wings, and may not be possible at all. Tip vortices can be controlled to increase the effective span, to generate rolling moment, to attenuate wing-rock, and to attenuate vortex-wing interactions. While there are different approaches for each application, opportunities for future research on turbulence ingestion, bleed, and excitation of vortex instabilities exist. Recent research also indicates that active and passive flow control can be used to manipulate the afterbody vortices in order to reduce the drag.