Graphene is a new two-dimensional material with interesting electronic properties and a wide range of applications. Graphene epitaxially grown on the Si-terminated surface of SiC is a good candidate to replace semiconductors in field-effect transistors. In this work we investigate the properties of epitaxial monolayer and bilayer graphene and develop a theoretical model used to describe the charge transfer between graphene and donors in SiC substrate. This model is then used to describe the behaviour of an epitaxial graphene-based transistor and the conditions for its operation. We also apply our model to understand the successful application of epitaxial graphene in quantum resistance metrology and to describe the effect of bilayer patches on the resistance quantization. Finally, we study how the ordering of adatoms on top of mechanically exfoliated graphene due to RKKY interaction affects the transport properties of graphene.