  We study charge transport in one-dimensional graphene superlattices created
by applying layered periodic and disordered potentials. It is shown that the
transport and spectral properties of such structures are strongly anisotropic.
In the direction perpendicular to the layers, the eigenstates in a disordered
sample are delocalized for all energies and provide a minimal non-zero
conductivity, which cannot be destroyed by disorder, no matter how strong this
is. However, along with extended states, there exist discrete sets of angles
and energies with exponentially localized eigenfunctions (disorder-induced
resonances). It is shown that, depending on the type of the unperturbed system,
the disorder could either suppress or enhance the transmission. Most remarkable
properties of the transmission have been found in graphene systems built of
alternating p-n and n-p junctions. This transmission has anomalously narrow
angular spectrum and, surprisingly, in some range of directions it is
practically independent of the amplitude of fluctuations of the potential.
Owing to these features, such samples could be used as building blocks in
tunable electronic circuits. To better understand the physical implications of
the results presented here, most of our results have been contrasted with those
for analogous wave systems. Along with similarities, a number of quite
surprising differences have been found.
