Graphene has a linear energy momentum dispersion and its Fermi velocity is vf=10^8 cm/s. This high carrier velocity and its perfect two-dimensional structure make it suitable for high speed electronic devices. In this work, we study the carrier transport in graphene and quasi-one dimensional graphene nanoribbons. The current-carrying capability in graphene under high fields is investigated by numerical simulations. The simulations reveal the roles of the hot-phonon effct and carrier-carrier scatterings in graphene under high fields. The effect of line edge roughness on mobility in sub-10 nm graphene nanoribbons is studied analytically. The results indicate the mobility in sub-10 nm graphene nanoribbons is limited by edge roughness scatterings and agree with experimental work. In addition, we explore inter-band tunneling in graphene and graphene nanoribbons and the current-voltage characteristics of their p-n junctions are calculated. Finally, an optical-phonon limited velocity model is extended from carbon-based materials to III-nitride semiconductors, which have comparable optical phonon scattering rates. The electron-phonon interaction in graphene and III-Nitride semiconductors have similarities characterized by light mass atoms (C or N). Thus, high-field transport in both materials have similarities which enable analytical modeling of radio frequency performance in these materials. GaN-based transistor performance is studied based on the model.