The NA62 experiment at the CERN SPS, designed to measure the branching ratio of the K+ → π+νν with a decay in-flight technique, collected data in 2016-2018. New results on rare kaon decays from the analysis of 2018 data, the largest data set so far collected, will be presented. The result represents the most accurate measurement so far achieved of this ultra-rare decay. Thanks to the huge sample of kaon decays NA62 can also put stringent limits on lepton number and lepton flavour violating decays and on the heavy neutral lepton production.