Probing Supersymmetric Flavor Models with $\epsilon'/\epsilon$

We discuss the supersymmetric contribution to $\epsilon'/\epsilon$ in various supersymmetric flavor models. We find that in alignment models the supersymmetric contribution could be significant while in heavy squark models it is expected to be small. The situation is particularly interesting in models that solve the flavor problems by either of the above mechanisms and the remaining CP problems by means of approximate CP, that is, all CP violating phases are small. In such models, the standard model contributions cannot account for $\epsilon'/\epsilon$ and a failure of the supersymmetric contributions to do so would exclude the model. In models of alignment and approximate CP, the supersymmetric contributions can account for $\epsilon'/\epsilon$ only if both the supersymmetric model parameters and the hadronic parameters assume rather extreme values. Such models are then strongly disfavored by the $\epsilon'/\epsilon$ measurements. Models of heavy squarks and approximate CP are excluded.