The quantities $\epsilon_K^\prime$ and $\epsilon_K$
measure the amount of direct and indirect CP violation in $K\to
\pi\pi$ decays, respectively. Using the recent lattice results
from the RBC and UKQCD Collaborations and a new compact
implementation of the $\Delta S=1$ renormalization group
evolution we predict
$
\mbox{Re} \frac{\epsilon_{K}'}{\epsilon_{K}} = \left(1.06 \pm 5.07 \right) \times
10^{-4} $
in the Standard Model. This value is $2.8\,\sigma$ below the
experimental value of
$
\mbox{Re} \frac{\epsilon_{K}'}{\epsilon_{K}} =
\left(16.6 \pm 2.3 \right) \times 10^{-4}.
$
In generic models of new physics the well-understood $\epsilon_K$
precludes large contributions to $\epsilon_K^\prime$, if the new
contributions enter at loop level. However, one can resolve the tension in $\epsilon_{K}'/\epsilon_{K}$ within the Minimal Supersymmetric Standard Model. To this end two features of supersymmetry are crucial:
First, one can have large isospin-breaking contributions (involving the strong instead of the weak interaction) which enhance
$\epsilon_K^\prime$. Second the Majorana nature of gluinos permits a
suppression of the MSSM contribution to $\epsilon_K$, because two box
diagrams interfere destructively.