Weak Matrix Elements on the Lattice: Recent Developments in K-Physics

Some recent developments in the calculation of weak matrix elements on the lattice are reviewed. In particular, we concentrate on the application of MPSTV non-perturbative renormalization method to the operators relevant to kaon physics. The chiral behaviour of the $B_K$ parameter and the long-standing question of the $\mathrm{\Delta }I=1\mathrm{/}2$ rule are discussed.