  We theoretically investigate Coulomb drag in a system of two parallel
monolayers of graphene. Using a Boltzmann equation approach we study a variety
of limits ranging from the non-degenerate interaction dominated limit close to
charge neutrality all the way to the Fermi liquid regime. In the non-degenerate
limit we find that the presence of the passive layer can largely influence the
conductivity of the active layer despite the absence of drag. This induces a
non-trivial temperature behavior of the single layer conductivity and
furthermore suggests a promising strategy towards increasing the role of
inelastic scattering in future experiments. For small but finite chemical
potential we find that the drag resistivity varies substantially as a function
of the ratio of inelastic and elastic scattering. We find that an extrapolation
from finite chemical potential to zero chemical potential and to the clean
system is delicate and the order of limits matters. In the Fermi liquid regime
we analyze drag as a function of temperature $T$ and the distance $d$ between
the layers and compare our results to existing theoretical and experimental
results. In addition to the conventional $1/d^4$-dependence with an associated
$T^2$-behavior we find there is another regime of $1/d^5$-dependence where drag
varies in linear-in-$T$ fashion. The relevant parameter separating these two
regimes is given by $\bar{d}=T d/v_F$ ($v_F$ is the Fermi velocity), where
$\bar{d} \ll1$ corresponds to $T^2$-behavior, while $\bar{d}\gg1$ corresponds
to $T$-behavior.
