Type-I seesaw provides the framework for "standard" leptogenesis, in which the baryon asymmetry of the Universe is entirely determined by the dynamics of the lightest right-handed neutrino. If one departures from this picture, other well-motivated scenarios for leptogenesis can be defined. Of particular interest are those based on either type-II or type-III seesaw. In this talk I will discuss leptogenesis in these frameworks, in both the unflavored and the flavored regimes. Finally, I will comment on the impact that Majoron-induced right-handed neutrino scattering might have on the B-L asymmetry.