We study the electronic structure of the ground and several low-lying states of the CeF molecule using Dirac-Fock-Roothaan (DFR) and four-component relativistic single and double excitation configuration interaction (SDCI) calculations in the reduced frozen-core approximation (RFCA). The ground state and two low-lying excited states are calculated to have (4f)(1)(5d)(1)(6s)(1) configurations with Omega = 3.5, 4.5, and 3.5, and the resulting excitation energies, To, are, respectively, 0.319 and 0.518 eV. The experimental configurations for these states arc the same, although the experimental To values are similar to 0.3 eV smaller than those calculated. Experimentally, the red-degraded band was observed to be 2.181 eV above the ground state, having the configuration (4f)(1)(5d)(1)(6p)(1) with Omega = 4.5. The calculation for this state gives 2.197 eV and configuration (4f)(1.0)(5d)(1.7)(6p)(0.3) with Omega = 4.5. We found that Omega, R-e, and nu(1-0) obtained by CI agree well with experiment. Bonding between the Ce and the F is highly ionic. The 4f, 5d, and 6s valence electrons are localized at the Ce+ ion, because they are attracted by the Ce4+ ion core, and are excluded from the bonding region because of the electronic cloud around the negatively charged fluoride anion. The bonding in the ground and excited states of the CeF molecule is significantly influenced by the 6s and 5d electron distributions between the Ce and the F.