The NA62 experiment at CERN collected the world's largest data set of charged kaon decays in 2016-2018 (Run1), leading to the first measurement of the branching ratio of the ultra-rare $K^+ \to \pi^+ \nu \bar{\nu}$ decay. An overview of the latest NA62 results on precision measurements based on Run1 data is presented.
An analysis of the flavor-changing neutral current $K^+ \to \pi^+ \mu^+ \mu^-$ decay, based on about $28 \times 10^3$ signal events with negligible background contamination, leads to the most precise determination of the branching ratio and of the form factor.
The radiative kaon decay $K^+ \to \pi^{o} e^+ \nu \gamma$ ($K_{e3\gamma}$) is studied with a data sample of $\mathcal{O}(10^5)$ $K_{e3\gamma}$ candidates with sub-percent background contamination. The most precise measurements of the branching ratio and T-asymmetry are achieved.
New preliminary results are obtained from an analysis of the $K^+ \to \pi^+ \gamma \gamma$ decay using data collected with a minimum-bias trigger. The sample, about 15 times larger than the previous largest one, leads to an unprecedented sensitivity.