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

Time-dependent transport in open systems based on quantum master equations