Rare Higgs decays, Higgs BSM and HH in ATLAS and CMS

The Higgs boson discovery signed a fundamental step in our comprehension of the Standard Model of elementary particles. Since then the ATLAS and CMS collaborations moved their focus from a discovery strategy to the study of the properties of the new boson also looking for possible hints of new physics. In these ten years enormous progress has been made in measuring the mass of the Higgs boson and its couplings to the other particles, arriving to extremely rare decays like those into a pair of muons or c quarks. Latest updates on object reconstruction and analysis strategies have brought many improvements also in the measurement of the Higgs boson self-coupling and the latest results have shown the possibility of improving this measurement well beyond what is given by an increased integrated luminosity.