  In this book article effects related to the vertical transport in weakly
coupled multiple quantum wells are reviewed. A self-contained microscopical
model for the calculation of the well-to-well currents without any fittings
parameters is presented. The model exhibits the well-known peaks in the
current-field relation in quantitative agreement with experiments. This local
current-field relation is used as an input for the calculation of the transport
in the extended structure consisting of many periods. Here both the formation
of stationary field domains as well as self-sustained current oscillations are
found in good agreement with experimental data. The underlying physics of these
nonlinear phenomena is discussed in detail.
