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The two-dimensional material graphene and its relatives have recently revolutionized the field of solid state physics. Despite its theoretical assessment as a monolayer of graphite since the 1940s, this model 2D system still holds a plethora of open questions with regard to fundamental research as well as technological applications. In order to further the understanding of this exciting material, this thesis is concerned with the study of local structural and electronic properties of graphene. The electronic structure of graphene, marked by the six Dirac cones, i.e. the touching points of valence and conduction band, at the corners of the Brillouin zone, is strongly influenced by the nature of and the interaction with its surroundings. In this thesis, several model systems are chosen, thus enabling the investigation of graphene/metal as well as graphene/semiconductor interfaces. Depending on the substrate under consideration, different in-situ preparation techniques had to be chosen and adjusted for optimal fabrication results. By means of scanning tunnelling microscopy and spectroscopy, the effect of lateral confinement on the energy spectrum of graphene was comparatively studied for extended and constricted graphene nanostructures on the noble metal (111) surfaces of Au and Ag, which were prepared by the intercalation technique on epitaxially grown, well-defined graphene/Ir(111) patches. While extended graphene sheets solely exhibited conventional intervalley scattering, additional features were observed in quasiparticle interference of confined structures. The shape of these features confirmed the strong influence of the flake edge configuration, the presence of defects as well as the coupling to the underlying substrate and was attributed to the inclusion of additional scattering channels between the transverse modes of the confined systems by comparison with tight-binding calculations. Furthermore, the influence of the strongly Rashba-split surface state of BiAg2 on the electronic structure of graphene was investigated, thereby testing whether the proximity to the spin-split BiAg2 might enhance the spin-orbit coupling strength of graphene itself. While no significant splitting larger than the measurement uncertainty could be observed in graphene, an unexpected shift of the BiAg2 surface state was determined and explained by an inward relaxation of the Bi atoms into the thick Ag intercalation layer at the interface triggered by the presence of graphene. Bandstructure investigations of graphene yielded an n-doping similar to the case of graphene/Ag(111) and a Fermi velocity of approxminately 1 · 106 m/s. Graphene monolayer growth on semiconducting Ge(110) from an atomic carbon source was established due to the limited catalytic activity and subsequently investigated with the help of several surface sensitive techniques. Depending on the growth temperature, different rotational domains were observed. Only one domain orientation was preserved for annealing temperatures near the substrate boiling point. The associated electronic structure was mapped out with the help of quasiparticle interference on the local scale and by different varieties of photoelectron spectroscopy at the macroscopic scale. Graphene preserved its linear dispersion relation, with a renormalized Fermi velocity at low temperatures attributable to the dielectric constant of Ge. Signatures of a segregation of Sb dopant atoms from the Ge bulk were observed at the interface in both photoelectron and local tunnelling measurements resulting in an n-doping of the flat graphene layer. published |