The formation of graphene on the (0001) surface of SiC (the Si-face) is studied by atomic force microscopy, low-energy electron microscopy, and scanning tunneling microscopy/spectroscopy. The graphene forms due to preferential sublimation of Si from the surface at high temperature, and the formation has been studied in both high-vacuum and 1-atm-argon environments. In vacuum, a few monolayers of graphene forms at temperatures around 1400°C, whereas in argon a temperature of about 1600°C is required in order to obtain a single graphene monolayer. In both cases considerable step motion on the surface is observed, with the resulting formation of step bunches separated laterally by ≳10 μm. Between the step bunches, layer-by-layer growth of the graphene is found. The presence of a disordered, secondary graphitic phase on the surface of the graphene is also identified.