This article outlines the content of the April 2004 issue of MRS Bulletin on Advances in Carbon Nanotubes. Essentially, carbon nanotubes are self-assembling nanostructures constructed of sheets of hexagonal-shaped carbon atoms rolled up into cylinders. Carbon nanotubes have attracted a great deal of attention as model systems for nanoscience and for potential applications. The special interest in carbon nanotubes stems from their unique structure and properties: their very small size (down to ∼0.42 nm in diameter); the possibility for carbon nanotubes to be metallic or semiconducting, depending on their geometrical structure; their exceptional properties of ballistic transport; their extremely high thermal conductivity and high optical polarizability; and the possibilities of high structural perfection. Research in the carbon nanotube field has now advanced to the stage where a good understanding of the structure and many of the basic properties are in place, together with much appreciation of their interrelation. On the other hand, major gaps in basic knowledge remain, with the major obstacles confronting the carbon nanotube field being the lack of a detailed understanding of the nanotube growth mechanism and control of the synthesis process to produce nanotubes with a desired diameter and chirality. The brief review of the carbon nanotube field by leading experts in this issue comes at an opportune time. Many exciting results on the structural, electronic, optical, and transport properties of these tiny well-ordered structures have already been achieved, and the research is well enough developed to assess present progress and identify new research directions waiting to be explored.