  A highly unconventional superconducting state with a spin-singlet
$d_{x^2-y^2}\pm id_{xy}$-wave, or chiral d-wave, symmetry has recently been
proposed to emerge from electron-electron interactions in doped graphene.
Especially graphene doped to the van Hove singularity at 1/4 doping, where the
density of states diverges, has been argued to likely be a chiral d-wave
superconductor. In this review we summarize the currently mounting theoretical
evidence for the existence of a chiral d-wave superconducting state in
graphene, obtained with methods ranging from mean-field studies of effective
Hamiltonians to angle-resolved renormalization group calculations. We further
discuss multiple distinctive properties of the chiral d-wave superconducting
state in graphene, as well as its stability in the presence of disorder. We
also review means of enhancing the chiral d-wave state using proximity-induced
superconductivity. The appearance of chiral d-wave superconductivity is
intimately linked to the hexagonal crystal lattice and we also offer a brief
overview of other materials which have also been proposed to be chiral d-wave
superconductors.
