Graphene can be grown by thermal decomposition of SiC(0001) surfaces [1,2]. Graphene on SiC is one of the best candidates for application in electronics because wafer-scale single crystalline graphene can be epitaxially grown on the semi-insulating substrate. For the controlled production of high-quality graphene on SiC, atomic-scale understanding of the growth process is needed. Roughly speaking, the growth process is driven by the sublimation 40of silicon atoms from the SiC surface and the subsequent rearrangement of the remaining carbon atoms into a densely packed honeycomb structure. In this chapter, we summarize the graphene growth mechanisms at the atomic scale revealed by high-resolution transmission electron microscope (HRTEM) observations combined with molecular-dynamics calculations based on density-functional tight-binding (DFTB) method. The graphene growth mechanism differs on different crystallographic surfaces, such as the Siand C-faces. We also describe the possible atomic structures of graphene on SiC and their basic electronic properties.