This book describes initial efforts, as part of the new Strategic Technology Institute (STI) on carbon electronics, to model and simulate the performance of graphene field-effect transistors (FETs) using macroscopic descriptions that are classical for semiconductor devices. It is argued that the underlying physics that differentiates these devices from their normal semiconductor-based counterparts is most clearly revealed by non-computer-intensive descriptions that allow the designer to compare their behaviour with that of their well-studied semiconductor counterparts. Because it admits a reasonable description of both the lateral and vertical field and transport functionality of the FET structure, the gradual-channel approximation is key to this approach.