Carbon nanotubes and graphene provide high carrier mobility for ballistic transport, high carrier velocity for fast switching, and excellent mechanical and thermal conductivity. As a result, they are widely considered as next generation candidate materials for nanoelectronics. In this thesis, I first propose a physics-based semi-analytical model for Schottky-barrier (SB) carbon nanotube (CNT) and graphene nanoribbon (GNR) transistors. The model reduces the computational complexity in the two critical but time-consuming steps, namely the calculation of the tunneling probability and the self-consistent evaluation of the surface potential in the transistor channel. Since SB-type CNT and GNR transistors exhibit ambipolar conduction that is not preferable in digital applications, I further propose a semi-analytical model for the double-gate transistor structure that is able to control the ambipolar conduction in-field. Future directions, including the modeling of new CNT and GNR devices and novel circuits based on the in-field controllability of ambipolar conduction, will also be described.