  We review the current status of the leptogenesis scenario originally proposed
by Akhmedov, Rubakov and Smirnov (ARS). It takes place in the parametric regime
where the right-handed neutrinos are at the electroweak scale or below and the
CP-violating effects are induced by the coherent superposition of different
right-handed mass eigenstates. Two main theoretical approaches to derive
quantum kinetic equations, the Hamiltonian time evolution as well as the
Closed-Time-Path technique are presented, and we discuss their relations. For
scenarios with two right-handed neutrinos, we chart the viable parameter space.
Both, a Bayesian analysis, that determines the most likely configurations for
viable leptogenesis given different variants of flat priors, and a
determination of the maximally allowed mixing between the light, mostly
left-handed, and heavy, mostly right-handed, neutrino states are discussed.
Rephasing invariants are shown to be a useful tool to classify and to
understand various distinct contributions to ARS leptogenesis that can dominate
in different parametric regimes. While these analyses are carried out for the
parametric regime where initial asymmetries are generated predominantly from
lepton-number conserving, but flavor violating effects, we also review the
contributions from lepton-number violating operators and identify the regions
of parameter space where these are relevant.
