Standard Model and SMEFT Higgs theory overview

After more than a decade from its discovery, the Higgs boson remains at the centre of the particle physics programme. While its couplings to vector bosons and third-generation fermions have been measured with impressive precision, the structure of the Higgs potential, the self-couplings, and the interactions with first- and second-generation fermions are still poorly constrained. This contribution summarises recent theoretical progress in precision predictions in Higgs physics, the interpretation of these results in Effective Field Theories (EFTs), and the current and future prospects to probe light Yukawa couplings at the LHC and beyond.