Historically important to build the Standard Model (SM) of particle physics, rare kaon decays are still a privileged tool to look beyond it. The main reasons to continue the study of rare kaon decays are testing the CKM quark mixing and CP-violation paradigm, making quantitative comparisons with the $B$ sector and searching for explicit violations of the SM. Current research focuses mostly on $ K \to \pi \nu \bar{\nu}$ decays which are predicted with good accuracy within the SM and beyond. Experimentally, these decays, especially the one of the charged kaon, have a long history. Their theoretical importance is matched only by their experimental difficulty. NA62 is the CERN experiment at the SPS built to study precisely $ K^+ \to \pi^+ \nu \bar{\nu}$ and other rare decays. Results based on the full 2016-2018 data set will be presented.
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