  The availability of high-intensity kaon beams at the J-PARC Hadron
Experimental Facility and the CERN SPS North Area, together with the abundant
forward production of kaons at the LHC, gives rise to unique possibilities for
sensitive tests of the Standard Model in the quark flavor sector. Precise
measurements of the branching ratios for the flavor-changing neutral current
decays $K\to\pi\nu\bar{\nu}$ can provide unique constraints on CKM unitarity
and, potentially, evidence for new physics. Building on the success of the
current generation of fixed-target experiments, initiatives are taking shape in
both Europe and Japan to measure the branching ratio for
$K^+\to\pi^+\nu\bar\nu$ to ~5% and for $K_L\to\pi^0\nu\bar\nu$ to ~20\%
precision. These planned experiments would also carry out lepton flavor
universality tests, lepton number and flavor conservation tests, and perform
other precision measurements in the kaon sector, as well as searches for exotic
particles in kaon decays. Meanwhile, the LHCb experiment is ready to restart
data taking with a trigger upgrade that will vastly increase its sensitivity
for rare $K_S$ decays and complementary hyperon decays. We overview the
initiatives for next-generation experiments in kaon physics in Europe and
Japan, identifying potential contributions from the US high-energy physics
community.
