  Vanilla leptogenesis within the type I seesaw framework requires the mass
scale of the right-handed neutrinos to be above 10^9 GeV. This lower bound can
be avoided if at least two of the sterile states are almost mass degenerate,
which leads to an enhancement of the decay asymmetry. Leptogenesis models that
can be tested in current and upcoming experiments often rely on this resonant
enhancement, and a systematic and consistent description is therefore necessary
for phenomenological applications. In this review article, we give an overview
of different methods that have been used to study the saturation of the
resonant enhancement when the mass difference becomes comparable to the
characteristic width of the Majorana neutrinos. In this limit, coherent flavor
transitions start to play a decisive role, and off-diagonal correlations in
flavor space have to be taken into account. We compare various formalisms that
have been used to describe the resonant regime and discuss under which
circumstances the resonant enhancement can be captured by simplified
expressions for the CP asymmetry. Finally, we briefly review some of the
phenomenological aspects of resonant leptogenesis.
