A review of the present experimental status of the $K \to \pi \nu \overline{\nu}$ ($K_{\pi \nu \nu}$) and other kaon decay analyses at experiments NA62 (CERN) and KOTO (J-PARC) is given.
The $K_{\pi \nu \nu}$ decay is one of the best candidates among the rare meson decays for indirect searches for new physics in the mass ranges complementary to those accessible by current accelerators. The Standard Model (SM) prediction of the branching fraction ($\mathcal{B}$) of the $K_{\pi \nu \nu}$ decay is lower than $10^{-10}$ in both neutral and charged modes. The NA62 experiment aims to measure the $\mathcal{B}$ of the charged mode with better than 10\% precision. Three candidate events, compatible with the SM prediction, have been observed from a sample of 2.12$\times 10^{12}$ $K^+$ decays collected in 2016 and 2017 by NA62. More than twice the statistics is available in the 2018 dataset currently being analysed. The KOTO experiment in Japan aims to measure $\mathcal{B}$($K_L \to \pi^0 \nu \overline{\nu}$) using a technique similar to NA62, but with much lower momentum. In the first dataset taken in 2015 zero signal candidate events were observed. The current status of the analysis of the 2016-2018 dataset with 1.4 times more data is presented.
Finally, the most recent results of other physics analyses at the NA62 experiment are summarised.