Status of searches for rare kaon decays at NA62 \& HIKE

Recent results from searches for rare kaon decays with the NA62 experiment at CERN are reported, together with the future prospects. A future experiment HIKE, to go beyond NA62, has been proposed to push kaon physics to an unprecedented frontier. The HIKE timescale and expected performance are described. Among the NA62 results, the measurement of the branching ratios of the flavour changing neutral current K⁺→π⁺μ⁺μ⁻ and the radiative non leptonic K⁺→π⁺γγ decays are reported, upper limits are given for lepton flavor and lepton number violating decays K⁺→μ⁻ν e⁺e⁺ and K⁺→π⁻π⁰ e⁺e⁺. A search for new physics in the branching ratio of the decay K⁺→π⁺ e⁺e⁻e⁺e⁻ is presented