Summary: In this dissertation, I will present my research studies on rational fabrication of GNRs with sub-10 nm width by employing nanowire as etch mask. Taking a step further, I will demonstrate a new graphene nanostructure-graphene nanomesh as a mimic of GNR network. This nanomesh structure introduces finite size effect into a large sheet of graphene while retaining the two-dimensional nature, and therefore may be advantageous in practical device fabrication and integration. Based on the advance of our fabrication method, I will show the first experimental observation of a dramatic enhancement of the conductance in a GNR field-effect transistor by a perpendicular magnetic field. Very large negative MR of nearly 100% with conductance enhanced over 10,000 times was observed at low temperatures; and more than 50% remained at room temperature. Similar magnetotransport behavior was also observed in graphene nanomesh device. The observed large MR was attributed to the complex interplay between edge roughness, quantum confinement and the formation of cyclotron orbits. These findings demonstrate interesting magnetotransport properties in graphene nanostructures, and can open up exciting new opportunities for a new generation of magneto-electronic devices.