We review the use of interatomic potentials to describe the bulk and surface behavior of carbonate materials. Interatomic pair potentials, describing the Ca2+-O interactions and the C-O bonding of the CO 32- anion group, are used to evaluate the lattice, elastic, dielectric, and vibrational data for calcite and aragonite. The resulting potential parameters for the carbonate group were then successfully transferred to models of the structures of rhombohedral carbonates of Mn, Fe, Mg, Ni, Zn, Co, and Cd. Simulations of the (101̄4) cleavage surface of calcite, magnesite, and dolomite show that these surfaces undergo relaxation leading to the rotation and distortion of the carbonate group with associated movement of cations. The influence of water on the surface structure has been investigated for monolayer coverage. The extent of carbonate group distortion is greater for the dry surfaces compared to the hydrated surfaces, and for the dry calcite relative to that for dry dolomite or magnesite. Point defect calculations for the doping of calcite indicate an increase in defect formation energy with increasing size of the substituting divalent ion. Migration energies for Ca, Mg, and Mn in calcite suggest a strong preference for diffusion along pathways roughly parallel to the c-axis rather than along the ab-plane.