Neutrino masses are evidence for physics beyond the Standard Model. Nevertheless, they cannot indicate by themselves what is the new underlying physics. Are there new -exotic- neutrino and/or charged lepton signals within reach, that may help to elucidate the origin of neutrino masses? We will discuss the present situation with a rather model-independent approach. The implications of Minimal Flavour Violation (a model-independent framework very successful in the quark sector) will be also discussed.