The study of lepton flavour violating (LFV) processes offers a unique tool to shed light on new physics. After introducing the main features of the scenario, we address the constraints on the seesaw parameters arising from the requirements of compatibility with low-energy data (neutrino masses and mixings, bounds on LFV decays and charged lepton electric dipole moments). We discuss with some detail the constraints on the seesaw parameters arising from the imposition of a successful baryon asymmetry of the Universe via thermal leptogenesis, when charged lepton flavours are taken into account. Finally, we consider hints on SUSY and seesaw parameters which can be derived from a potential measurement of low-energy neutrino mixings and LFV branching ratios.