Models for Majorana neutrino masses can be classified according to the level in perturbation theory at which the effective dimension five operator LLHH is realized. The possibilities range from the tree-level up to the three-loop level realizations. We discuss some general aspects of this approach and speculate about a model independent classification of the possible cases. Among all the realizations, those in which the effective operator is induced by radiative corrections open the possibility for lepton number violation near -or at- the electroweak scale. We discuss some phenomenological aspects of two generic radiative realizations: the Babu-Zee model and supersymmetric models with bilinear R-parity violation.