Lepton Flavour Violation in the charged lepton sector (CLFV) is forbidden in the Minimal Standard model and strongly suppressed in extensions of the model to include finite neutrino mixing. On the other hand, a wide class of Supersymmetric theories, even coupled with Grand Unification models (SUSY-GUT models), predict CLFV processes at a rate within the reach of new experimental searches operated with high resolution detectors at high intensity accelerators. As the Standard model background is negligible, the observation of one or more CLFV events would provide incontrovertible evidence for physics beyond Standard model, while a null effect would severely constrain the set of theory parameters. Therefore, a big experimental effort is curren...