Crab cavity systems for future colliders *

KEKB was the first facility to implement the crab crossing technique in 2007, for the interaction of electron and positron beams. The High Luminosity Large Hadron Collider (HL-LHC) project envisages the use of crab cavities for increasing and levelling the luminosity of proton-proton collisions in LHC. Crab cavities have also been proposed and studied for future colliders like CLIC, ILC and eRHIC. This contribution will focus on the near and far future of crab cavities for particle colliders.