In this paper we discuss and review results of recent studies of epitaxial growth of graphene on silicon carbide. The presentation is focused on high quality, large and uniform layer graphene growth on the SiC(0 0 0 1) surface and the results of using different growth techniques and parameters are compared. This is an important subject because access to high-quality graphene sheets on a suitable substrate plays a crucial role for future electronics applications involving patterning. Different techniques used to characterize the graphene grown are summarized. We moreover show that atomic hydrogen exposures can convert a monolayer graphene sample on SiC(0 0 0 1) to bi-layer graphene without the carbon buffer layer. Thus, a new process to prepare large, homogeneous stable bi-layer graphene sheets on SiC(0 0 0 1) is presented. The process is shown to be reversible and should be very attractive for various applications, including hydrogen storage.