Theoretical status of ε'/ε

I give a detailed introduction into the theoretical formalism for ε'/ε, which measures direct CP-violation in K → ππ 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 ε'/ε are pointed out: A small strange quark mass, an enhancement of the hadronic parameter B6(1/2) from the σ resonance, an underestimate of isospin breaking and possible new physics contributions in the s-bardZ-vertex and the s-bard-gluon-vertex