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I will consider the problem of charge transport through mesoscopic devices such as quantum pumps, disordered conductors or simple junctions. A central aspect is the statistics of the transferred charge, where the quantum nature of the current carriers becomes relevant. Using algebraic techniques of open quantum systems, I will present a general treatment of the question. Moreover, a rigorous study of the relation between the moments of charge transport and current fluctuations will also allow us to resolve an old controversy on the time ordering of current correlators.