Employing multireference variational methods (MRCI), we have constructed full potential-energy curves for the ground state (X (3)Delta) and forty excited states of the diatomic carbide, FeC. For all states we report potential-energy curves, bond lengths, dissociation energies, dipole moments, and certain spectroscopic constants, trying at the same time to get some insight on the bonding mechanisms with the help of Mulliken populations and valence-bond-Lewis diagrams. For the X (3)Delta state at the MRCI level of theory, we obtain a dissociation energy D-e=86.7 kcal/mol at a bond length r(e)=1.581 Angstrom. These values compare favorably to the corresponding experimental ones, D-e=91.2+/-7 (upper limit) kcal/mol and r(e)=1.5924 Angstrom. The first excited state ((1)Delta) is predicted to be 9.7 kcal/mol above the X-state as compared to an experimental value of 9.786 kcal/mol.