Abstract
The NA62 experiment at CERN, dedicated to measurements of
ultra-rare decays of the charged kaon with the decay-in-flight
technique, collected a large data set corresponding to 6 10^{12}
kaon decays during its first run in 2016-2018. A summary of physics
results using this data sample is presented, including the flagship
analysis, measurement of the K+-->pi+nunu decay rate, and searches
for lepton number and lepton flavour violating decays. Prospects for
future NA62 data-taking, beginning in 2021, are also discussed.