Graphene, the single layer of hexagonally coordinated carbon, is a two-dimensional material with many unusual properties; its physical realization a few years ago has caused a storm of activities in the solid state physics and materials science communities. The intriguing “massless Dirac Fermion” character of its charge carriers renders graphene a unique study object in condensed matter physics, and we discuss how surface-related techniques such as photoemission, STM and LEED play a prominent role in these investigations. We report on experimental studies of the growth and electronic structure of epitaxial single and few layer graphene on silicon carbide. The unusual band structure of single layer graphene and its evolution as layers are added towards bulk graphite is studied. In the special case of the bilayer, the opening of a gap by inducing an asymmetry through the influence of doping is examined. Finally, the influence of many body processes on the spectral function is discussed on the basis of high resolution photoemission data. The discussion of these aspects gives a comprehensive overview of the electronic structure of graphene as examined by experiment.