In order to describe properly the physics above the electroweak scale, wewill discuss next the so-called gauge invariant Standard Model Effective Theory (SMEFT). This theory became very popular in view of the fact that the LHC until now did not discover directly any new particles. It offers a model independent formulation of NP beyond the SM in terms of operators that are invariant under the full SM gauge group. This is a very important framework, and many techniques developed in this decade in the context of SMEFT are crucial for a serious phenomenological applications in order to obtain model independent results. Moreover, SMEFT technology plays an important role in the derivation of predictions in concrete models as well.We will see this in this chapter and subsequent chapters of our book. But already in this chapter we will discuss implications of SMEFT in a number of general NP scenarios in which only a subset of operators is relevant. Moreover, we will present a few general formulas valid for any NP model, in particular the one for the ratio epsilon'/epsilon.