  We perform a thorough study of thermal leptogenesis adding finite temperature
effects, RGE corrections, scatterings involving gauge bosons and by properly
avoiding overcounting on-shell processes. Assuming hierarchical right-handed
neutrinos with arbitrary abundancy, successful leptogenesis can be achieved if
left-handed neutrinos are lighter than 0.15 eV and right-handed neutrinos
heavier than 2 10^7 GeV (SM case, 3sigma C.L.). MSSM results are similar.
  Furthermore, we study how reheating after inflation affects thermal
leptogenesis. Assuming that the inflaton reheats SM particles but not directly
right-handed neutrinos, we derive the lower bound on the reheating temperature
to be T_RH > 2 10^9 GeV. This bound conflicts with the cosmological gravitino
bound present in supersymmetric theories. We study some scenarios that avoid
this conflict: `soft leptogenesis', leptogenesis in presence of a large
right-handed (s)neutrino abundancy or of a sneutrino condensate.
