  We report on recent experimental results from transport measurements with
large Hall bars made of high mobility GaAs/AlGaAs heterostructures. Thermally
activated conductivities and hopping transport were investigated in the integer
quantum Hall regime. The predominant transport processes in two dimensions are
discussed. The implications of transport regime on prefactor universality and
on the relation between $\rho_{xx}$ and $\rho_{xy}$ are studied. Particularly
in the Landau level tails, strictly linear dependence
$\delta\rho_{xy}(\rho_{xx})$ was found, with pronounced asymmetries with
respect to the plateau centre. At low temperatures, Ohmic (temperature
dependent) as well as non-Ohmic (current dependent) transport were investigated
and analysed on the basis of variable-range hopping theory. The non-Ohmic
regime could successfully be described by an effective electron temperature
model. The results from either the Ohmic transport or from a comparison of
Ohmic and non-Ohmic data allowed to determine the localization length $\xi$ in
two different ways. The observed divergence of $\xi(\nu)$ with the filling
factor $\nu$ approaching a Landau level centre, is in qualitative agreement
with scaling theories of electron localization. The absolute values of $\xi$
far from the $\rho_{xx}$ peaks are compared with theoretical predictions. On
one hand, discrepancies between the $\xi$ results obtained from the two
experimental methods are attributed to an inhomogeneous electric field
distribution. Extrapolation yields an effective width of dominant potential
drop of about $100 mu$m. On the other hand, our analysis suggests a divergence
of the dielectric function $\epsilon_{r} \propto \xi^{\beta}$ with $\beta
\simeq 1$.
