Carbon nanotube sorting, i.e., the separation of a mixture of tubes into different electronic types and further into species with a specific chirality, is a fascinating problem of both scientific and technological importance. It is one of those problems that are easy to describe but difficult to solve. Single-stranded DNA forms stable complexes with carbon nanotubes and disperses them effectively in water. A particular DNA sequence of alternating guanine (G) and thymine (T) nucleotides ((GT)_n, with n = 10 to 45) self-assembles into an ordered supramolecular structure around an individual nanotube, in such a way that the electrostatic properties of the DNA-carbon nanotube hybrid depend on tube structure, enabling nanotube separation by anion-exchange chromatography. This review provides a summary of the separation of metallic and semiconducting tubes, and purification of single (n, m) tubes using the DNA-wrapping approach. We will present our current understanding of the DNA-carbon nanotube hybrid structure and separation mechanisms, and predict future developments of the DNA-based approach.