  Massive neutrinos and leptonic mixings have provided the first evidence of
flavour violation in the lepton sector, opening a unique gateway to many new
phenomena. Among the latter, one finds processes violating lepton number,
charged lepton flavours, or even the universality of lepton flavours. These
very rare transitions can be studied in high-intensity facilities, and if
observed, constitute a clear sign of New Physics. After a brief review of the
experimental status of dedicated searches, we comment on the prospects of
several well-motivated models of neutrino mass generation to several of the
above mentioned observables, also discussing how the interplay of
high-intensity observables and neutrino data can shed light on the underlying
New Physics model.
