Various types of interactions between halogen (X) and pi moiety (X-pi interaction) including halogen bonding play important roles in forming the structures of biological, supramolecular, and nanomaterial systems containing halogens and aromatic rings. Furthermore, halogen molecules such as X-2 and CX4 (X = Cl/Br) can be intercalated in graphite and bilayer graphene for doping and graphene functionalization/modification. Due to the X-pi interactions, though recently highly studied, their structures are still hardly predictable. Here, using the coupled-cluster with single, double, and noniterative triple excitations (CCSD(T)), the Moller-Plesset second-order perturbation theory (MP2), and various flavors of density functional theory (DFT) methods, we study complexes of benzene (Bz) with halogen-containing molecules X-2 and CX4 (X = Cl/Br) and analyze various components of the interaction energy using symmetry adapted perturbation theory (SAPT). As for the lowest energy conformers (S1), X-2-Bz is found to have the T-shaped structure where the electropositive X atom-end of X-2 is pointing to the electronegative midpoint of CC bond of the Bz ring, and CX4-Bz has the stacked structure. In addition to this CX4 Bz (S1), other low energy conformers of X-2-Bz (S2/S3) and CX4-Bz (S2) are stabilized primarily by the dispersion interaction, whereas the electrostatic interaction is substantial. Most of the density functionals show noticeable deviations from the CCSD(T) complete basis set (CBS) limit binding energies, especially in the case of strongly halogen-bonded conformers of X-2-Bz (S1), whereas the deviations are relatively small for CX4-Bz where the dispersion is more important. The halogen bond shows highly anisotropic electron density around halogen atoms and the DFT results are very sensitive to basis set. The unsatisfactory performance of many density functionals could be mainly due to less accurate exchange. This is evidenced from the good performance by the dispersion corrected hybrid and double hybrid functionals. B2GP-PLYP-D3 and PBE0-TS (Tkatchenko-Scheffler)/D3 are well suited to describe the X-pi interactions adequately, close to the CCSD(T)/CBS binding energies (within similar to 1 kJ/mol). This understanding would be useful to study diverse X-pi interaction driven structures such as halogen containing compounds intercalated between 2-dimensional layers.