In this thesis, we theoretically investigate electronic, magnetic and optical properties of disordered graphene quantum dots. The numerical calculations are performed using a combination of tight-binding, mean-field Hubbard and configuration interaction methods. We focus on the effects of long-range disorder and electron-electron interactions on the optical properties and the effects of atomic defect related short-range disorders and electron-electron interactions on Anderson type localization and the magnetic properties of hexagonal armchair graphene quantum dots. For the case of long-range disorder, we show that, when the electron-hole puddles are present, tight-binding method gives a poor description of the low-energy absorption spectra compared to meanfield and configuration interaction calculation results. As the size of the graphene quantum dot is increased, the universal optical conductivity limit can be observed in the absorption spectrum. When disorder is present, calculated absorption spectrum approaches the experimental results for isolated monolayer of graphene sheet. On the other hand, for the case of short-range related disorder, we observe that randomly distributed defects with concentrations between 1-5% of the total number of atoms leads to electronic localization alongside magnetic puddle-like structures. We show that localization length is not affected by magnetization if there is an even distribution of defects between the two sublattices of the honeycomb lattice. However, for an uneven distributions, localization is found to be significantly enhanced.