The spin-orbit interaction as a relativistic interaction destroys the ideal relativistic "touching cones" of electronic dispersion at the Dirac point in graphene. It opens a gap of tenths of micro eV. It turns out that this essentially sp material has its spin-orbit coupling derived almost exclusively from d-orbitals [1]. Few-layer graphene structures may be potentially useful for optical and transport applications, due to the possibility of electrical control of the band gaps. We show, by performing first-principles full potential linearized augmented plane waves calculations, that the spin-orbit physics in these structures and in graphite derives essentially from monolayer graphene. In particular, the spin splitting of the bands is due to the spin-orbit coupling of the d-orbitals. These give a splitting of the order of 24 microeV at the K point, as in graphene. Breaking the spatial inversion symmetry by a transverse electric field does not change this (intrinsic) picture, unlike what we know from graphene. Functionalization of graphene by adatoms or admolecules gives rise to an enhancement of spin splitting due to new principal linear spin-orbit band splittings driven by the breaking of the local pseudospin inversion symmetry and the emergence of spin flips on the same sublattice [2].