  Heavy right handed neutrinos could not only explain the observed neutrino
masses via the seesaw mechanism, but also generate the baryon asymmetry of the
universe via leptogenesis due to their CP-violating interactions in the early
universe. We review recent progress in the theoretical description of this
nonequilibrium process. Improved calculations are particularly important for a
comparison with experimental data in testable scenarios with Majorana masses
below the TeV scale, in which the heavy neutrinos can be found at the LHC, in
the NA62 experiment, at T2K or in future experiments, including SHiP, DUNE and
experiments at the FCC, ILC or CEPC. In addition, the relevant source of
CP-violation may be experimentally accessible, and the heavy neutrinos can give
a sizable contribution to neutrinoless double $\beta$ decay. In these low scale
leptogenesis scenarios, the matter-antimatter asymmetry is generated at
temperatures when the heavy neutrinos are relativistic, and thermal corrections
to the transport equations in the early universe are large.
