A wealth of experimental and theoretical research over the previous decade has demonstrated the anomalous properties of carbon nanotubes, a novel material synthesized in the previous decade and having great potential application to nanotechnology. We review our local-density functional approach for helical chain polymers that has been used extensively to study the electronic and structural properties of carbon nanotubes as well as other technologically important polymers. We provide detailed first-principles results for the density of states of carbon nanotubes supporting the validity of a simple Hu¨ckel-level picture of their Fermi level properties. ©2001 American Institute of Physics.