The NA62 experiment at CERN SPS was designed to measure BR(K+ -> pi+ nu nu-bar) with in-flight decays, a novel technique for this channel. NA62 took its first physics data in 2016, reaching the sensitivity to the decay at the Standard Model BR. The experiment collected 10 times more statistics in 2017 and a similar amount of data is expected from the 2018 run.
The result on K+ to pi+ nu nu-bar from the full 2016 data set and the latest extrapolation and background evaluation from the 2017 data set will be presented. Prospects for improvements to be achieved with the full data set will also be discussed.
A large sample of charged kaon decays into final states with multiple charged particles was also collected in 2016-2018. The sensitivity to a number of Lepton Flavour and Lepton Number violating K+ decays provided by this data set is an order of magnitude beyond the current state of the art. The latest results of the search for K+ → π- l+ l+ (l=mu, e) decays and prospect for the search of K+ → π- mu+ e+ and K+ → π+ mu- e+ processes will be reviewed.
Recent results on production searches of Dark Photons in neutral pion decays at NA62 will also be outlined, together with sensitivity results for production and decay searches of Heavy Neutral Leptons, Axion-Like Particles and prospects for future data taking at the NA62 experiment.