  We discuss the various incarnations of a gauged B-L symmetry: 1) unbroken, it
features Dirac neutrinos, neutrinogenesis to create the baryon asymmetry of our
Universe, and a potentially light Z' boson; 2) broken by two units, we obtain
the standard case of Majorana neutrinos, seesaw and thermal leptogenesis; 3)
broken by four units, we find Dirac neutrinos with lepton-number-violating
interactions, which can give rise to a new Dirac leptogenesis mechanism. We
review and discuss the signatures distinguishing the three scenarios.
