New physics limits from kaon decays

Searches for lepton flavour violation and lepton number violation in kaon decays by the NA62 and NA48/2 experiments at CERN are presented. A new measurement of the ratio of charged kaon leptonic decay rates $R_K=\mathrm{\Gamma }(K_{e2})\mathrm{/}\mathrm{\Gamma }(K_{\mu 2})$ to sub-percent relative precision is discussed. An improved upper limit on the lepton number violating $K^{\pm }\to {\pi }^{\mp }{\mu }^{\pm }{\mu }^{\pm }$ decay rate is also reported. The future 10% precision measurement of the branching ratio of the ultra-rare kaon decay $K^{+}\to {\pi }^{+}\nu \bar{\nu }$ with the NA62 experiment is finally reviewed.