Publisher Summary This chapter discusses the electronic properties of carbon nanotubes. Graphite is a semimetal, a highly unusual electronic material with a unique Fermi surface. As a result, the additional quantization present in nanoscale graphitic fragments is a fascinating subject, resulting in electronic properties, which cannot be duplicated by nano wires composed of normal metals or semiconductors. Graphite has layered structure composed of parallel planes of sp2-bonded carbon atoms called “graphene” layers. These layers are 0.34 nm apart and only interact via weak, van der Waals forces. The valence and conduction bands of all materials are drawn as continuous but are actually composed of closely spaced, discrete states. Graphene begins as a 2D material, but it too may be further quantized by slicing a narrow strip from the sheet. In this case, the allowed electronic states constitute a line of points, or “band,” sliced from the graphene 2D band structure. Because nanotubes exhibit many interesting electronic properties, a wide range of electronic applications are proposed and investigated in the chapter.