  R-parity conservation is an ad-hoc assumption in the most popular versions of
supersymmetric scenarios. Hence R-parity violation (RPV) not only is allowed
but, if induced by bilinear terms (bRPV), it also provides an explanation for
the observed neutrino masses and mixing. Here bRPV models are discussed, giving
emphasis on the $\mu$-from-$\nu$ supersymmetric standard model, which is
characterised by a rich Higgs sector that easily accommodates a 125-GeV Higgs
boson. The phenomenology of such models at the Large Hadron Collider is
reviewed and some recent results obtained by LHC experiments are presented. The
possibility to extend such analyses to probe bRPV scenarios with a gravitino
dark matter candidate is also explored.
