The stability of gold iodides in the oxidation state +I and +III is investigated at the ab initio and density functional level using relativistic and nonrelativistic energy-adjusted pseudopotentials for gold and iodine. The calculations reveal that relativistic effects stabilize the higher oxidation state of gold as expected, that is Au2I6 is thermodynamically stable at the relativistic level, whilst at the nonrelativistic level the complex of two iodine molecules weakly bound to both gold atoms in Au2I2 is energetically preferred. The rather low stability of AuI3 with respect to dissociation into AuI and I2 will make it difficult to isolate this species in the solid state as (possibly) Au2I6 or detect it by matrix-isolation techniques. The monomer AuI3 is Jahn-Teller distorted from the ideal trigonal planar (D3h) form, but adopts a Y-shaped structure (in contrast to AuF3 and AuCl3), and in the nonrelativistic case can be described as I2 weakly bound to AuI. Relativistic effects turn AuI3 from a static Jahn-Teller system to a dynamic one. For the yet undetected gas-phase species AuI accurate coupled-cluster calculations for the potential energy curve are used to predict vibrational-rotational constants. Solid-state density functional calculations are performed for AuI and Au2I6 in order to predict cohesive energies.