Leptogenesis offers a very attractive explanation for the origin of the baryon asymmetry of the universe. Such scenarios based on leptonic CP–violation can be realized already within minimalistic seesaw extensions of the standard model. Apart from model building issues the answer to the question of whether a given particle theory can explain the observed baryon number density depends also on the detailed statistical evolution of the asymmetry. The CP–violation within a given model leads to an asymmetry only if it is accompanied by an out–of–equilibrium evolution in the early universe. Most existing analyses employ Boltzmann–like equations (BEs) to describe it. In this context fundamental issues arise which can be addressed in the framework of non–equilibrium quantum field theory (NEQFT). Here, the relevance of quantum and medium effects for thermal leptogenesis is investigated. Within the 2PI–formalism of NEQFT, questions such as that for the justification of the particle picture arise naturally in subsequent approximations when BEs are to be derived. This specific problem is particularly important in the case of resonant leptogenesis where the relevant particle states are almost degenerate in mass. It is found that Boltzmann like equations can (only) be obtained in certain cases. But it is then possible to account for corrections due to quantum and medium effects.