Precision tests of Standard Model with leptonic and semileptonic kaon decays

Till the middle of 2004 it appeared that the unitarity relation Vud^2+Vus^2+Vub^2=1 might not hold at the 2.3sigma level. At that time, however, Vus was inferred from old experimental data. Since then, a large experimental and theoretical effort has been invested leading to a removal of the problem. Thanks to the new and improved measurements by BNL-E865, KLOE, KTeV, ISTRA+ and NA48, the Kl3 decay rate moved up so that Vus is now consistent with unitarity. On the theory side, much progress has been made in order to tame the systematic uncertainties related to the computation of the Kl3 form factors. This joint progress allowed to assess the validity of the CKM unitarity relation at the level of less than $1%. Recent measurements of kaon decays contributing to the determination of Vus, Vus/Vud are summarized, and up-to-date evaluations of Vusf0 and Vus are presented. In addition, we discuss the sensitivity of Kl3 and Kl2 decays to various scenarios of physics beyond Standard Model.