Rare kaon decays are among the most sensitive probes of both heavy and light new physics
beyond the Standard Model (SM) description thanks to high precision of the Standard Model
predictions, availability of very large datasets, and the relatively simple decay topologies. The
NA62 experiment at CERN is a multi-purpose high-intensity kaon decay experiment, and carries
out a broad rare-decay and hidden-sector physics programme. Recent NA62 results on searches
for violation of lepton flavour and lepton number in kaon decays, and searches for production in
hidden-sector mediators in kaon decays, are presented. Future prospects of these searches are
discussed.

