The rare K decays are one of the main tools for the exploration of flavor physics, being the only clean window into the (s --> d) sector. In case of New Physics discovery at LHC, they would become essential in solving the "inverse problem", i.e. to reconstruct the right theory out of experimental data. In this talk, we will first explain what makes those modes so clean theoretically, by reviewing the various theoretical ingredients entering their BR predictions in the SM. Then, in the second part, their exceptional sensitivity to New Physics effects will be illustrated by specific examples, namely the MSSM -with large or moderate tangent beta, and with or without the minimal flavor violation hypothesis- and the little Higgs model.
