------------------------------------------------------------------------- `'on physics from lattice simulations Abstract: In the last years, enormous progress have been made by the lattice community, in particular in the kaon sector. The simulations have become realistic and new techniques have been developed, allowing us to have a better control on the systematic errors, but also to access new quantities. I will present a selection of recent lattice results and their phenomenological impact in the quest for new physics. In particular I will report on the computation of K-> pi pi decays achieved by the RBC-UKQCD collaborations, which is relevant for the study of direct and indirect CP violation. The DeltaI=3/2 part of this computation has been performed with a realistic setup, and represents the first "ab initio" calculation of a hadronic weak decay. -------------------------------------------------------------------------