Critical experiments in fundamental Nuclear and High Energy Physics require for their realization intense, extremely focused hadron-hadron, lepton-lepton and hadron-lepton colliding beams. Luminosity increase by a few orders of value in upgraded existing and future collider complexes can be achieved by use of beam cooling techniques which are capable to increase the colliding beams density in phase space. We will describe the physics and technology of a variety of well established cooling techniques and as well as some novel conceptions, together with related R&D for high luminosity colliders. Recent progress on advancing high energy electron cooling, stochastic cooling and coherent electron cooling for hadron beams and ionization cooling for muon beams will be highlighted. Some critical questions about efficient organization of the interaction regions adequate to new quality levels of colliding beams (low emittance, very short bunches)  will be addressed and possible solutions (high repetition rate crab crossing bunches, extremely short achromatic collision area) discussed.