The NA62 experiment at the CERN Super Proton Synchrotron (SPS) is currently taking data to measure the ultra-rare decay K + → π + νν¯. The high-intensity setup, trigger flexibility, detector performance and high-efficiency vetoes make NA62 also suitable for direct searches of long-lived, beyond-the-Standard-Model particles, such as Heavy Neutral Leptons (HNLs), Axion-Like Particles (ALPs) and Dark Photons (DPs); moreover, many rare and forbidden decays are studied at NA62. The status of all these searches is reviewed, together with prospects for future data taking at NA62 after the CERN Long Shutdown 2 (LS2).
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