The molecular structures of all gold mono- and trihalides and of their dimers have been calculated at the B3LYP, MP2, and CCSD(T) levels of theory by using relativistic pseudopotentials for all atoms except fluorine. Our computations support the experimental observation that the relative stability of the monohalides increases from the fluoride toward the iodide, while the stability trend of the trihalides is the opposite. The potential energy surface (PES) of all gold trihalides has been investigated. These molecules are typical Jahn-Teller systems; the trigonal planar D3h-symmetry geometry does not correspond to the minimum energy structure for any of them. At the same time, the amount and character of their Jahn-Teller distortion changes gradually from AuF3 to AuI3. The minimum energy geometry is a T-shaped structure for AuF3 and AuCl3, with a Y-shaped transition-state structure. For AuI3, the Y-shaped structure lies lower than the T-shaped structure on the PES. For AuBr3 and AuI3, neither of them is the global minimum but instead an L-shaped structure, which lies outside the Jahn-Teller PES. This structure can be considered to be a donor-acceptor system, or a closed-shell interaction, with I2 acting as donor and AuI as acceptor. The dimers of gold monohalides have very short gold-gold distances and demonstrate the aurophilic interaction. The dimers of the trihalides are planar molecules with two bridging halogen atoms.