  Recent developments in thermal leptogenesis are reviewed. Neutrino mixing
data favor a simple picture where the matter-anti matter asymmetry is generated
by the decays of the heavy RH neutrinos mildly close to thermal equilibrium
and, remarkably, in the full non relativistic regime. This results into
predictions of the final baryon asymmetry not depending on the initial
conditions and with minimized theoretical uncertainties. After a short outline
of a geometrical derivation of the CP asymmetry bound, we derive analytic
bounds on the lightest RH neutrino mass and on the absolute neutrino mass
scale. Neutrino masses larger than 0.1 eV are not compatible with the minimal
leptogenesis scenario. We discuss how the results get just slightly modified
within the minimal supersymmetric standard model. In particular a conservative
lower bound on the reheating temperature, T_R \gtrsim 10^9 GeV, is obtained in
the relevant effective neutrino mass range tilde{m}_1 \gtrsim 3x10^{-3} eV. We
also comment on the existence of a `too-short-blanket problem' in connection
with the possibility of evading the leptogenesis neutrino mass bound.
