The NA62 experiment at the CERN SPS recorded in 2007 a large sample of
$K^+ \rightarrow \mu^+ \nu_\mu $ decays. A peak search in the missing
mass spectrum of this decay is performed. In the absence of observed
signal, the limits obtained on $\mathcal{B}(K^+ \rightarrow \mu^+ \nu_h )$ and
on the mixing matrix element $|U_{\mu4}|$ are reported. The upgraded
NA62 experiment started data taking in 2015. About 5$\times 10^{11}
K^+$ decays have been recorded so far to measure the branching ratio
of the $K^+ \rightarrow \pi^+ \nu\overline{\nu}$ decay. Preliminary
results from the $K^+ \rightarrow \pi^+ \nu\overline{\nu}$ analysis
based on about 5$\%$ of the 2016 statistics are reported.