  An important class of approaches to the description of electronic transport
through molecules and quantum dots is based on the master equation. We discuss
various formalisms for deriving a master equation and their interrelations. It
is shown that the master equations derived by Wangsness, Bloch, and Redfield
and by Koenig et al. are equivalent. The roles of the large-reservoir and
Markov approximations are clarified. The Markov approximation is traced back to
nonzero bias voltage and temperature, whereas interactions and the
corresponding rapid relaxation in the leads are shown to be irrelevant for the
transport under certain conditions. It is explained why the T-matrix formalism
gives incomplete results except for diagonal density operators and to second
order in the tunneling amplitudes. The time-convolutionless master equation is
adapted to tunneling problems and a diagrammatic scheme for generating
arbitrary orders in the tunneling amplitudes is developed.
