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We evaluate the potential of carbon nanotubes (CNTs) as the basis for a new nanoelectronic technology. After briefly reviewing the electronic structure and transport properties of CNTs, we discuss the fabrication of CNT field-effect transistors (CNTFETs) formed from individual single-walled nanotubes (SWCNTs), SWCNT bundles, or multiwalled (MW) CNTs. The performance characteristics of the CNTFETs are discussed and compared to those of corresponding silicon devices. We show that CNTFETs are very competitive with state-of-the-art conventional devices. We also discuss the switching mechanism of CNTFETs and show that it involves the modulation by the gate field of Schottky barriers at the metal-CNT junctions. This switching mechanism can account for the observed subthreshold and vertical scaling behavior of CNTFETs, as well as their sensitivity to atmospheric oxygen. The potential for integration of CNT devices is demonstrated by fabricating a logic gate along a single nanotube molecule. Finally, we discuss our efforts to grow CNTs locally and selectively, and a method is presented for growing oriented SWCNTs without the involvement of a metal catalyst.