This thesis discusses methods for the comparatively mild covalent functionalization of graphene. Several graphene models were investigated: polycyclic aromatic hydrocarbons (PAHs), chemical vapor deposition (CVD)-graphene on SiO2/Si substrate, graphite foil, graphite flakes, kish graphite and highly oriented pyrolytic graphite. The PAHs were viewed as graphene edge analogs with the following molecules representing different edge motifs: pyrene, perylene, benzo[a]pyrene, benzo[e]pyrene, triphenylene, acenapthylene, and anthracene. Ozone was used in combination with different solvents to functionalize PAHs, graphite, and CVD-graphene on SiO2/Si. Ozonation in water or methanol resulted in trapping of the carbonyl oxide intermediate that was formed in the reaction, producing a variety of functional groups. Ozonation in hydrogen peroxide solution with sonication promoted radical formation, possibly resulting in edge-oxidation of graphite. The regioselectivity for addition reactions (ozonolysis) and electrophilic aromatic substitution reactions with graphene edges is discussed. To achieve functionalization of the basal plane of graphite or graphene, white light irradiation was used in combination with several transfer hydrogenation reagents. Formic acid treatment under irradiation resulted in the expected hydrogenation, whereas iso-propanol treatment resulted in iso-propanol attachment to the graphene. The developed methods provide opportunities for graphene functionalization without the need for metal based reagents or harsh conditions.