Status and prospects of rare decay searches at NA62

The $K^+ \to \pi^+ \nu \overline{\nu}$ decay is a golden mode for flavour physics. Its branching ratio is predicted with high precision by the Standard Model to be less than $10^{-10}$, and this decay mode is highly sensitive to indirect effects of new physics up to the highest mass scales. A new measurement of the $K^{+}\rightarrow\pi^{+}\nu\bar{\nu}$ decay by the NA62 experiment at CERN using data collected in 2021 and 2022 is presented. This new dataset was collected after modifications to the beamline and detectors and at a higher instantaneous beam intensity with respect to the previous 2016$-$2018 data taking. Using the complete datasets from 2016$-$2022, for the first time, the $K^+ \to \pi^+ \nu \overline{\nu}$ decay is observed with a significance exceeding $5\sigma$.