Graphene, a two dimensional single layer of graphite, attracts a lot of attention of researchers around the globe due to its remarkable physical properties and application potential. The origin can thereby be found in the peculiar electronic structure since graphene is a zero gap semi-conductor with a linear energy dispersion in the vicinity of the Fermi level. Consequently, the charge carriers in graphene mimic massless Dirac Fermions which brings principles of quantum electrodynamics and exotic effects like Klein tunneling into a bench-top experiment. Modifying the electronic and/or crystal structure structure by functionalization might therefore as well lead to new tantalizing physical properties, novel compound materials based on graphene like graphane (fully hydrogenated graphene) or flourographene (fluorinated graphene), and ultimately new applications. In this work, the influences on the electronic structure of graphene are investigated with photoemission spectroscopies after covalent functionalization by atomic hydrogen and ionic functionalization with potassium. Regarding hydrogenation, the formation of tunable bandgap is observed along with a full recovery of the electronic properties of graphene upon removing the hydrogen by thermal annealing. Using high resolution x-ray photoemission and molecular dynamics simulations, the formation of a C4H structure is predicted for substrate supported graphene at a saturation H-coverage of 25%, due to a preferential para- arrangement of hydrogen atoms. In fully electron doped, hydrogenated graphene the formation of dispersionless hydrogen impurity state is observed with angle-resolved photoemission spectroscopy. This flat state is extended over the whole Brillouin zone and according to calculations not localized. Potassium-doped graphene shows a similar doping level as its 3D parent component, the graphite intercalation compound KC8. Investigating the electron-phonon coupling in doped graphene, by direct derivation of the Eliashberg-function, shows an asymmetric coupling strength along the high-symmetry directions in the Brillouin Zone of graphene. In the K-M direction additional low energetic contributions could be identified which may originate from out-of-plane phonon modes. Regarding the electron-phonon-coupling strength of the high energy in-plane phonon modes a reasonable agreement with theoretical predictions is found.