The XXV International Symposium on Lattice Field Theory

CKM-unitarity, direct and indirect CP-violation and the D I = 1/2 rule in full lattice QCD are the focus of this talk. To this end I will discuss and compare recent lattice results for leptonic, semi-leptonic and non-leptonic decays of the kaon and neutral kaon mixing and I will motivate current best estimates fK / f p = 1.198(10) , f K p+ (0) = 0.964(5) and ˆBK = 0.720(39). Moreover new theoretical advances that will improve the quality of these computations in the future will be discussed