  Oxide heterostructures allow for detailed studies of two-dimensional
electronic transport phenomena. Here different facets of magnetotransport in
selected spin-orbit coupled systems are analyzed and characterized by their
single-band and multi-band behavior, respectively. Experimentally, temperature
and magnetic field dependent measurements in the single-band system
BaPbO$_3$/SrTiO$_3$ reveal strong interplay of weak antilocalization (WAL) and
electron-electron interaction (EEI). Within a scheme which treats both, WAL and
EEI, on an equal footing a strong contribution of EEI at low temperatures is
found which suggests the emergence of a strongly correlated ground state.
Furthermore, now taking multi-band effects into account as they appear, e.g.,
in the model system LaAlO$_3$/SrTiO$_3$, theoretical investigations predict a
huge impact of filling on the topological Hall effect in systems with
intermingled bands. Already weak band coupling produces striking deviations
from the well-known Hall conductivity that are only explainable in a fully
quantum mechanical treatment which builds upon the hybridization of
intersecting Hofstadter bands.
