Abstract: The Standard Model Effective Field Theory (SMEFT) provides a systematic framework for parameterizing heavy new physics in a model-independent way. A central ingredient for precision analyses is the renormalization group evolution of Wilson coefficients across energy scales. The recent computation of the two-loop beta-functions in the SMEFT enables genuine next-to-leading order (NLO) studies of this evolution. In this seminar, I will discuss the two-loop SMEFT anomalous dimension matrix and its phenomenological impact, focusing in particular on electroweak precision observables and the role of NLO running in the interpretation of precision data. I will then present ongoing work towards a complete NLO pipeline connecting the SMEFT to the low-energy effective field theory (LEFT), combining two-loop running in both theories with one-loop matching. This framework paves the way for consistent NLO analyses connecting high-scale new physics to low-energy observables.