  Estimates of the CP violating observable $\varepsilon'/\varepsilon$ have
gained some attention in the past few years. Depending on the long-distance
treatment used, they exhibit up to $2.9\sigma$ deviation from the
experimentally measured value. Such a deviation motivates the investigation of
New Physics (NP) effects in the process $K\to\pi\pi$. In my talk I will review
the Standard Model (SM) prediction for $\varepsilon'/\varepsilon$, with a
special focus on the Dual QCD approach. On the NP side, I will discuss a recent
computation of the hadronic matrix elements of NP operators. Furthermore a
master formula for BSM effects in $\varepsilon'/\varepsilon$ is presented.
Finally, a treatment of $\varepsilon'/\varepsilon$ using the SM effective
theory (SMEFT) will be discussed together with possible correlations to other
observables.

High Energy Physics - Phenomenology;High Energy Physics - Experiment;High Energy Physics - Lattice