Neutrino masses demand for new physics beyond the Standard Model. The
seesaw mechanism offers a way to generate naturally small neutrino
masses. In this seminar we discuss the phenomenology associated to
the three types of seesaw models using the effective field theory
approach and show that its effects are relevant only if the new
physics scale is relatively low. We discuss a framework where this is
realized and use present experimental constraints to put bounds on the
seesaw parameters. We focus in particular on two aspects of the
phenomenology of the type-III seesaw model, namely the rare lepton
decays and the anomalous magnetic moment of leptons. Finally we
discuss the possibility of discovering the responsible for neutrino
masses at the LHC.