  Electrons in the active region of a nanostructure constitute an open
many-body quantum system, interacting with contacts, phonons, and photons. We
review the basic premises of the open system theory, focusing on the common
approximations that lead to Markovian and non-Markovian master equations for
the reduced statistical operator. We highlight recent progress on the use of
master equations in quantum transport, and discuss the limitations and
potential new directions of this approach.
