The Rare Decays K → πνν̄ and KL → π0ℓ+ℓ−

Standard-model and possible New-Physics contributions can compete in magnitude in the rare Kaon decay modes K → πν and KL → π0l+l−. In particular the K → πν decays, the structure of short-distance physics is unclouded by non-perturbative, low-energy effects. This makes these decays excellent probes of New Physics. We review the status of the standard-model prediction of both K → πν and KL → π0l+l− decays and discuss the recent progress in the perturbative part of the K → πν decays.