In this thesis we investigate localization behavior of electronic states in bilayer graphene and bilayer graphene nanoribbon formed with the Bernal stacking in presence of diagonal disorder within the tight-binding model. Bilayer graphene is a semi-metal consisting of two coupled hexagonal lattices with inequivalent sites , and , on the bottom and top graphene sheets. Early proposals for the control of the electronic properties in graphene, such as the opening of gaps, were based on controlling its geometry by reducing it to nanoribbons. Nevertheless, current lithographic techniques that can produce such nanostructures do not have enough accuracy to cut graphene to Angstrom precision. As a result, graphene nanostructures unavoidably have rough edges which have strong effects in traort properties of nanoribbons. This can be accomplished in a bilayer graphene with an electric field applied perpendicular to the plane. It was shown theoretically and demonstrated experimentally that a bilayer graphene is the only material with semiconducting properties that can be controlled by electric field. Effect of disorder is similar to the applied electric field to the plane