  Electric transport in semiconductor superlattices is dominated by pronounced
negative differential conductivity. In this report the standard transport
theories for superlattices, i.e. miniband conduction, Wannier-Stark-hopping,
and sequential tunneling, are reviewed in detail. Their relation to each other
is clarified by a comparison with a quantum transport model based on
nonequilibrium Green functions. It is demonstrated how the occurrence of
negative differential conductivity causes inhomogeneous electric field
distributions, yielding either a characteristic sawtooth shape of the
current-voltage characteristic or self-sustained current oscillations. An
additional ac-voltage in the THz range is included in the theory as well. The
results display absolute negative conductance, photon-assisted tunneling, the
possibility of gain, and a negative tunneling capacitance.
