Many future particle colliders require beam crabbing to recover geometric luminosity loss from the nonzero crossing angle at the interaction point (IP). A first demonstration experiment of crabbing with hadron beams was successfully carried out with high energy protons. This breakthrough result is fundamental to achieve the physics goals of the high luminosity LHC (HL-LHC) and the future circular collider (FCC). The expected peak luminosity gain (related to collision rate) is 65% for HL-LHC and even greater for the FCC. Novel beam physics experiments with proton beams in CERN's Super Proton Synchrotron (SPS) were performed to demonstrate several critical aspects for the operation of crab cavities in the future HL-LHC including transparency with a pair of cavities, a full characterization of the cavity impedance with high beam currents, controlled emittance growth from crab cavity induced rf noise. © 2021 American Physical Society. All rights reserved.