Lepton number violation in 331 models

Different models based on the extended $SU(3{)}_{C}\ifmmode\times\else\texttimes\fi{}SU(3{)}_{L}\ifmmode\times\else\texttimes\fi{}U(1{)}_{X}$ (331) gauge group have been proposed over the past four decades. Yet, despite being an active research topic, the status of lepton number in 331 models has not been fully addressed in the literature, and furthermore many of the original proposals can not explain the observed neutrino masses. In this paper we review the basic features of various 331 models, focusing on potential sources of lepton number violation. We then describe different modifications which can be made to the original models in order to accommodate neutrino (and charged lepton) masses.