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 $R_K=\Gamma(K_{e2})/\Gamma(K_{\mu2})$ to sub-percent relative precision is discussed. An improved upper limit on the lepton number violating $K^\pm\rightarrow\pi^\mp\mu^\pm\mu^\pm$ decay rate is also reported. The future 10% precision measurement of the branching ratio of the ultra-rare kaon decay $K^+\rightarrow\pi^+\nu\bar{\nu}$ with the NA62 experiment is finally reviewed.