The interaction of beryllium with benzene, graphene and graphitic compounds involves multi-reference electronic states, Jahn-Teller distortion, charge transfer and van der Waals interactions. This is investigated herein using periodic and molecular models at different levels of theory: (i) the second-order Møller-Plesset (MP2) perturbation theory, (ii) the coupled cluster method with inclusion of single double and perturbative triple excitations (CCSD(T)), (iii) the complete active space self-consistent field (CAS-SCF) and (iv) the complete active space with perturbation theory truncated at the 2nd order (CAS-PT2). Molecular and periodic Density Functional Theory (DFT) methods are also used. The two major failures of DFT are addressed with regard to the beryllium benzene and graphene interaction: the degeneracy problem is the source of no specific problem while the delocalization error causes DFT with the Perdew Burke, Ernzerhof functional plus the Grimme correction (DFT/PBE-D2) to be over-binding by about 0.4 eV at a short-range. The agreement between DFT/PBE-D2 and wave-function based methods is nevertheless good; DFT/PBE-D2 provides an accurate description of the electronic structure of the system. By the end of this work, we shall get a better insight into the mechanisms leading beryllium to physisorb on graphene and to chemisorb into the bilayer of graphite.