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

CP violation and Kaon weak matrix elements from Lattice QCD