  Although not an intrinsic superconductor, it has been long--known that, when
intercalated with certain dopants, graphite is capable of exhibiting
superconductivity. Of the family of graphite--based materials which are known
to superconduct, perhaps the most well--studied are the alkali metal--graphite
intercalation compounds (GIC) and, of these, the most easily fabricated is the
C${}_8$K system which exhibits a transition temperature $\bm{T_c\simeq 0.14}
$K. By increasing the alkali metal concentration (through high pressure
fabrication techniques), the transition temperature has been shown to increase
to as much as $\bm 5 $K in C${}_2$Na. Lately, in an important recent
development, Weller \emph{et al.} have shown that, at ambient conditions, the
intercalated compounds \cyb and \cca exhibit superconductivity with transition
temperatures $\bm{T_c\simeq 6.5} $K and $\bm{11.5} $K respectively, in excess
of that presently reported for other graphite--based compounds. We explore the
architecture of the states near the Fermi level and identify characteristics of
the electronic band structure generic to GICs. As expected, we find that charge
transfer from the intercalant atoms to the graphene sheets results in the
occupation of the $\bm\pi$--bands. Yet, remarkably, in all those -- and only
those -- compounds that superconduct, we find that an interlayer state, which
is well separated from the carbon sheets, also becomes occupied. We show that
the energy of the interlayer band is controlled by a combination of its
occupancy and the separation between the carbon layers.
