Relativistic effective core potential quantum chemical investigations of molecular geometries, vibrational frequencies, and bond dissociation energies of cerium tri- and tetrahalides CeX3 and CeX4 (X = F, Cl) are presented. At RHF, MP2, and CASSCF levels of theory, CeF4 and CeCl4 possess stable tetrahedral (Td) geometries, and the calculated bond distances and vibrational frequencies lie very close to available electron diffraction and vibrational spectroscopy data. There is evidence of different stabilities of present tetrahalides toward the reductive elimination to CeX3. Thus, the very strong CeF3-F bond can be contrasted with the easier chlorine elimination to CeCl3. Five possible lower-lying electronic stales are associated with open-shell CeX3 halides, depending on the 4f orbital occupancy. The (4f(z)(3))(1) configuration represents the ground state, mostly due to the nonbonding nature of the corresponding atomic orbital whose electron density, perpendicular to the molecular plane, minimizes the electrostatic repulsion between the unpaired 4f metal electron and the halogen pairs. In agreement with experimental results, pyramidal structures (C-3v) are found for CeF3 for any of 4f(1) state at all levels of theory. By contrast, the relative stability of the planar and pyramidal structures of CeCl3 strongly depends on the adopted basis set, as well as on the effects of correlation terms.