Effective field theories (EFTs) are used to calculate contributions to low-energy precision observables in models with high-scale new physics (NP). In such situations, the NP model should be matched onto an appropriate EFT (often the SMEFT). In this seminar, I discuss how to organize the matching step in general and how the ideas can be extended to multi-loop calculations. I will also discuss how to extend the modern matching methods to theories with spontaneously broken gauge symmetries by working with a partially fixed background field gauge.