Theoretical status of epsilon'/epsilon

I give a detailed introduction into the theoretical formalism for epsilon'/epsilon, which measures direct CP-violation in K -> pi pi decays. The current status of hadronic matrix elements and the strange quark mass is discussed. Several possible explanations of the unexpectedly high experimental results for epsilon'/epsilon are pointed out: A small strange quark mass, an enhancement of the hadronic parameter B_6^(1/2) from the sigma resonance, an underestimate of isospin breaking and possible new physics contributions in the sdZ-vertex and the sd-gluon-vertex.