We review recent progress in the measurement and understanding of the electrical properties of individual metal and semiconducting single-wall carbon nanotubes. The fundamental scattering mechanisms governing the electrical transport in nanotubes are discussed, along with the properties of p-n and Schottky-barrier junctions in semiconductor tubes. The use of advanced nanotube devices for electronic, high-frequency, and electromechanical applications is discussed. We then examine quantum transport in carbon nanotubes, including the observation of quantized conductance, proximity-induced supercurrents, and spin-dependent ballistic transport. We move on to explore the properties of single and coupled carbon-nanotube quantum dots. Spin and orbital (isospin) magnetic moments lead to fourfold shell structure and unusual Kondo phenomena. We conclude with a discussion of unanswered questions and a look to future research directions.