The discovery of neutrino oscillations more than a decade ago called for an extension of the Standard Model (SM) that would generate neutrino masses and mixing. One of the simplest possibilities is the addition of fermionic gauge singlets or sterile neutrinos. TeV-scale realisations of this idea lead to a very rich phenomenology due to the mixing of the new fermions with the left-handed neutrinos of the SM and the large Higgs-neutrino-neutrino coupling. The experimental discovery of the Higgs boson at the LHC marked the start of multi-decade effort to measure its properties. We will discuss here how heavy sterile neutrinos give rise to new lepton flavour violating Higgs decays and corrections to the triple Higgs coupling, making this idea testable at current and future experiments.
