There are many reasons why one would want to form chemical attachments to the walls or ends of carbon nanotubes: these chemical bonds might be used to tailor the interaction of the nanotube with other entities, such as a solvent, a polymer matrix, or other nanotubes. The chemically functionalized nanotube might have mechanical or electrical properties that are different from those of the unfunctionalized nanotube and thus might be used as a chemical sensor or a nanometer-scale electronic device. The challenge is to find a way to reproducibly and reliably chemically alter carbon nanotubes that, like graphite, are fairly unreactive. The various methods used to date and the possible application of the resulting functionalized nanotubes is discussed in this review paper.