The non-observation of flavour violating transitions among charged leptons is understood within the Standard Model (SM) as a mere accident. The discovery of a Higgs boson around 125 GeV opens a new window to search for LFV phenomena via Higgs decays. It has been pointed out that low energy constraints still allow for sizable rates for such decays. In this talk I will discuss about this possibility in some detail, describing the rich complementarity between the intensity and the energy frontiers.