A  straightforward Supersymmetrization of the Standard Model results in a phenomenologically inconsistent theory in which Baryon and Lepton numbers are violated by
dimension 4 operators.
Suitable extensions of the Standard Model gauge symmetries can provide additional constraints on the allowed operators, in such a way that  R-parity conservation arises in a
natural way as an accidental symmetry.
In this framework, only Lepton number is mildly violated by super-renormalizable terms, allowing for small neutrino Majorana masses. After introducing the theoretical framework
for Supersymmetric Models without R-parity and without Lepton number, I will discuss some phenomenological relations between the parameters that give rise to neutrino masses and mixings, and certain lepton number violating decays of the stop (the superpartner of the top-quark) that would constitute an unmistakeable signature for these models.