Generation of the neutrino masses and leptogenesis (LG) in the Standard Model extended by the heavy Majorana fermions is considered. Classification of LG scenarios according to the new fermion mass spectra is given, where singlet-triplet LG is considered for the first time. The upper bound on the CP asymmetry relevant for LG with hierarchical heavy neutrinos (Davidson-Ibarr?a bound) is revised, and shown that in the case of one massless neutrino it essentially depends on the type of the light neutrino mass hierarchy. The resonant scenarios, which help to avoid the problem of extremely high reheating temperature in the early universe, are discussed. In particular, we present new simplified, generalized and detailed formulation of freed LG, which violates Davidson-Ibarra bound in a special class of models.