Catalytic decomposition of hydrocarbons on transition metals attracts a renewed interest as a route toward high-quality graphene prepared in a reproducible manner. Here we employ two growth methods for graphene on Ir(111), namely room temperature adsorption and thermal decomposition at 870–1470 K (temperature programmed growth (TPG)) as well as direct exposure of the hot substrate at 870–1320 K (chemical vapor deposition (CVD)). The temperature- and exposure-dependent growth of graphene is investigated in detail by scanning tunneling microscopy. TPG is found to yield compact graphene islands bounded by C zigzag edges. The island size may be tuned from a few to a couple of tens of nanometers through Smoluchowski ripening. In the CVD growth, the carbon in ethene molecules arriving on the Ir surface is found to convert with probability near unity to graphene. The temperature-dependent nucleation, interaction with steps and coalescence of graphene islands are analyzed and a consistent model for CVD growth is developed.