Status of lattice calculations of hadron matrix elements along with CP violation in B and in K systems is reviewed. Lattice has provided useful input which, in conjunction with experimental data, leads to the conclusion that CP-odd phase in the CKM matrix plays the dominant role in the observed asymmetry in B {yields} {psi}K{sub s}. It is now quite likely that any beyond the SM, CP-odd, phase will cause only small deviations in B-physics. Search for the effects of the new phase(s) will consequently require very large data samples as well as very precise theoretical predictions. Clean determination of all the angles of the unitarity triangle therefore becomes essential. In this regard B {yields} KD{sup 0} processes play a unique role. Regarding K-decays, remarkable progress made by theory with regard to maintenance of chiral symmetry on the lattice is briefly discussed. First application already provide quantitative information on B{sub K} and the {Delta}I = 1/2 rule. The enhancement in ReA{sub 0} appears to arise solely from tree operators, esp. Q{sub 2}; penguin contribution to ReA{sub 0} appears to be very small. However, improved calculations are necessary for {epsilon}{prime}/{epsilon} as there the contributions of QCD penguins and electroweak penguins largely seem …