  In this short review, I present the recent lattice computations of kaon weak
matrix elements relevant to $K \to \pi\pi$ decays and neutral kaon mixing.
These matrix elements are key to the theoretical determination of the CP
violation parameters $\epsilon$ and $\epsilon'$ . Impressive progress have been
achieved recently, in particular the first realistic computation of
$\epsilon'/\epsilon$ with physical kinematics has been reported in [1]. The
novelty is the $\Delta I = 1/2$ channel, whereas the $\Delta I = 3/2$
contribution is now computed at several values of the lattice spacing and
extrapolated to the continuum limit. I will also present the status of $B_K$
and discuss its error budget, with a particular emphasis on the perturbative
error. Finally I will review the matrix elements of neutral kaon mixing beyond
the standard model and will argue that the discrepancy observed by different
collaborations could be explained by the renormalisation procedure of the
relevant four-quark operators.
