The NA62 experiment at the CERN SPS aims to measure the branching ratio of
the rare decay K+→π+ννˉ with a relative precision of ∼10.
To achieve that goal, it is designed to be exposed to 1.2×1013K+
decays in its fiducial volume. The unprecedented K+ flux will lead to record
sensitivities to rare and forbidden decays of K+ and π0, including
those that violate lepton flavour or lepton number conservation. The expected
NA62 performances for lepton flavour conservation and lepton universality tests
are discussed. Relevant on-going or recently completed measurements from the
K± decay data sets collected by earlier kaon experiments at CERN (NA48/2
and NA62-RK​) are also presented.Comment: Talk given at the 1st Charged Lepton Flavour Conference, Lecce, May
201