A highly unconventional superconducting state with a spin-singlet dx2-y2+/-idxy-wave, or chiral d-wave symmetry has recently been suggested to emerge from electron-electron interactions in doped graphene. It has been argued that graphene doped to the van Hove singularity at 1/4 doping, where the density of states diverge, is particularly likely to 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 the 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 the 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.