  In order to address the baryon asymmetry in the Universe one needs to
understand the origin of baryon (B) and lepton (L) number violation. In this
article, we discuss the mechanism of baryogenesis via leptogenesis to explain
the matter-antimatter asymmetry in theories with spontaneous breaking of baryon
and lepton number. In this context, a lepton asymmetry is generated through the
out-of-equilibrium decays of right-handed neutrinos at the high-scale, while
local baryon number must be broken below the multi-TeV scale to satisfy the
cosmological bounds on the dark matter relic density. We demonstrate how the
lepton asymmetry generated via leptogenesis can be converted in two different
ways: a) in the theory predicting Majorana dark matter the lepton asymmetry is
converted into a baryon asymmetry, and b) in the theory with Dirac dark matter
the decays of right-handed neutrinos can generate lepton and dark matter
asymmetries that are then partially converted into a baryon asymmetry.
Consequently, we show how to explain the matter-antimatter asymmetry, the dark
matter relic density and neutrino masses in theories for local baryon and
lepton number.
