In this thesis, electronic, magnetic and optical properties of graphene nanoribbons are investigated within mean-field Hubbard model with two different disorder type; long and short range in finite and cyclic topology. First we investigated combined effect of electron-electron interaction effects and long range potential fluctuations. In both of the geometries, electron-electron interaction effects make edge states robust against disorders. Furthermore, surprisingly, strong enough disorder causes system to experience a phase transition from antiferromagnetically coupled edge states to ferromagnetic coupling in agreement with recent theoretical and experimental studies. Then, the stability of optical conductance under impurity effects, correlation between optical characteristic and magnetic phase of ZGNR is investigated, respectively. Similar to edge state density profile recovery, electronic interaction effects reduce the impurity induced peak around Fermi level. More importantly, we found distinct optical transitions due to edge-bulk mixed states around Fermi level that can be used to detect whether ZGNR is in antiferromagnetic or ferromagnetic phase. Finally, we investigated the disorder induced metalinsulator transition. Since, long range impurities protect the sublattice symmetry and leads to phenomena known as ”absence of backscattering”, there exist minimum conductivity for graphene. On the other hand, in order to model hydrogenation effects, we used short range impurity potential which breaks the sublattice symmetry. Using a time dependent tight binding model, we observed Anderson localization induced metal to insulator transition with a nanometer scale localization length for 2% hydrogen coverage. We found that, Anderson localization is stronger at high energy valence states since those states are more vulnerable to hydrogenation.