After the pioneering investigations into graphene-based electronics at Georgia Tech, great strides have been made developing epitaxial graphene on silicon carbide (EG) as a new electronic material. EG has not only demonstrated its potential for large scale applications, it also has become an important material for fundamental two-dimensional electron gas physics. Graphene is generally considered to be a strong candidate to succeed silicon as an electronic material. However, to date, it actually has not yet demonstrated capabilities that exceed standard semiconducting materials. One disadvantage of conventionally fabricated graphene devices is that nanoscopically patterned graphene tends to have disordered edges that severely reduce mobilities thereby obviating its advantage over other materials. The other disadvantage is that pristine graphene does not contain a band gap, which is critical for standard field effect transistor to operate. This thesis will show that graphene grown on structured silicon carbide surfaces overcomes the edge roughness and promises to provide an inroad into nanoscale patterning of graphene. High-quality ribbons and rings can be made using this technique.