Recent theoretical and computational advances have enabled the precision determination of multi-particle Standard Model amplitudes using lattice QCD. In particular the measure of direct CP-violation in kaon decays, $\epsilon'$, has now been computed with errors that are 40\% of the experimental value; this quantity is highly sensitive to BSM sources of CP-violation and may help shed light on the origin of the matter-antimatter asymmetry in the Universe. We will discuss this calculation of $\epsilon'$ and our present and future efforts in improving our result. We will also briefly discuss our ongoing calculations of other long-distance contributions to kaonic amplitudes sensitive to new physics.