  Extensive studies on thin films indicated a generic cubic current-voltage
$I-V$ dependence as a salient feature of charge transport by tunneling. A quick
glance at $I-V$ data for molecular junctions suggests a qualitatively similar
behavior. This would render model-based studies almost irrelevant, since,
whatever the model, its parameters can always be adjusted to fit symmetric
(asymmetric) $I-V$ curves characterized by two (three) expansion coefficients.
Here, we systematically examine popular models based on tunneling barrier or
tight-binding pictures and demonstrate that, for a quantitative description at
biases of interest ($V$ slightly higher than the transition voltage $V_t$),
cubic expansions do not suffice. A detailed collection of analytical formulae
as well as their conditions of applicability are presented to facilitate
experimentalists colleagues to process and interpret their experimental data by
obtained by measuring currents in molecular junctions. We discuss in detail the
limits of applicability of the various models and emphasize that uncritically
adjusting model parameters to experiment may be unjustified because the values
deduced in this way may fall in ranges rendering a specific model invalid or
incompatible to ab initio estimates. We exemplify with the benchmark case of
oligophenylene-based junctions, for which results of ab initio quantum chemical
calculations are also reported. As a specific issue, we address the impact of
the spatial potential profile and show that it is not notable up to biases V
somewhat larger than V_t, unlike at higher biases, where it may be responsible
for negative differential resistance effects.
