Atomistic computer-simulation techniques are used to investigate the defect and ion transport properties of the Hg-based superconductors. We focus our attention on the highest-T-c material, HgBa2Ca2Cu3O8+delta, for which we correctly reproduce the tetragonal structure using our potential model. Defect calculations predict the most favorable oxygen interstitial position as the O(4) [1/2 1/2 0] site on the Hg plane, in agreement with diffraction studies. We find significant local relaxation around this defect. The complex defect, which involves substitution of Cu for Hg, is also examined in some detail. We calculate exothermic energies for the hole-doping (oxidation) reaction in which oxygen excess (delta) is incorporated as doubly charged O(4) interstitials and compensated by hole formation. Oxygen diffusion is attributed to interstitial migration, and is predicted to be both rapid and anisotropic.