  NA62 is a fixed target kaon experiment at the CERN SPS which aims at
measuring the branching ratio of the $K^+\to\pi^+\nu\bar{\nu}$ decay with 10%
precision. This ultra-rare kaon decay is theoretically extremely clean and an
ideal place to look for physics beyond the Standard Model. The NA62 experiment
has been running in 2016-2018 and has accumulated a large amount of kaon
decays. The final result of the $K^+\to\pi^+\nu\bar{\nu}$ analysis using the
2016 dataset is discussed as well as prospects for the analysis of the 2017
dataset. NA62 also has sensitivity to various other rare and forbidden kaon
decays, as well as some hidden sector models. The results of a search for the
Lepton Number Violating decays $K^+\to\pi^-\ell^+\ell^+\ [\ell=e,\mu]$ is
presented, along with new limits on the existence of a dark photon.
