  We study the coupled dynamics of spin and charge currents in a
two-dimensional electron gas in the transport diffusive regime. For systems
with inversion symmetry there are established relations between the spin Hall
effect, the anomalous Hall effect and the inverse spin Hall effect. However, in
two-dimensional electron gases of semiconductors like GaAs, inversion symmetry
is broken so that the standard arguments do not apply. We demonstrate that in
the presence of a Rashba type of spin-orbit coupling (broken structural
inversion symmetry) the anomalous Hall effect, the spin Hall and inverse spin
Hall effect are substantially different effects. Furthermore we discuss the
inverse spin Hall effect for a two-dimensional electron gas with Rashba and
Dresselhaus spin-orbit coupling; our results agree with a recent experiment.
