Iridium thin films are grown by direct-current plasma magnetron sputtering, on MgO single-crystal substrates with various surface orientations, i.e. (100), (111), and (110). The surface morphology, the crystalline properties of the films, and the substrate-thin-film interface are investigated by atomic force microscopy, X-ray diffraction (XRD), focused ion beam scanning electron microscopy, and high-resolution transmission electron microscopy, respectively. The results reveal that hetero-epitaxial thin films with different crystallographic orientation and notable atomic scale smooth surface are obtained. From the XRD analysis, the following epitaxial relations are obtained: (1) (100)(Ir)||(100)(MgO) out-of-plane and [001](Ir)||[001](MgO) in-plane for Ir grown on MgO(100), (2) (110)(Ir)||(110)(MgO) out-of-plane and [1-10](Ir)||[1-10](MgO) in-plane for Ir grown on MgO(110), and (3) (111)(Ir)||(111)(MgO) out-of-plane and two variants for in-plane orientation [1-10](Ir)||[1-10](MgO) and [1-10](Ir)||[10-1](MgO), respectively, for Ir grown on MgO(111). Because of the large misfit strain (9.7%), the thin films are found to grow in a strain-relaxed state with the formation of geometrical misfit dislocations with a similar to 2.8-nm spacing, whereas thermal strain is stored upon cooling down from the growth temperature (600 degrees C). The best structural characteristics are obtained for the (111)-oriented films with a mosaicity of 0.3 degrees and vanishingly small lattice distortions. The (100)- and (110)-oriented films exhibit mosaicities of similar to 1.2 degrees and lattice distortions of similar to 1% which can be explained by the larger surface energy of these planes as compared to (111).