Searches for Lepton Flavour and Number Violation and Hidden Sector Particles at NA62

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.