Single-walled carbon nanotubes (SWCNTs) demonstrate a unique combination of optical, chemical, and physical properties that render them suitable for a variety of sensing applications. Their photostable near-infrared (nIR) fluorescence emissions are highly sensitive to perturbations in the surrounding SWCNT environment, enabling optical sensors with single-molecule detection limits. Despite these immanent advantages, SWCNTs lack the inherent molecular recognition capabilities required for selective sensing applications. One approach to tuning sensor selectivity is to engineer synthetic and biological wrappings that cover the nanotube's surface in a manner that limits chemical access to the surface to specific target analytes. Among the numerous possible wrappings, deoxyribonucleic acid (DNA) has emerged as the most studied polymeric wrapping. In addition to the sequence-dependent tunability DNA offers in engineering selectivity, DNA assumes a peculiar helical wrapping conformation along the SWCNT surface that has been the focus of many experimental and computational studies. In this review, we summarize some of the major findings in the field, focusing on the underlying molecular interactions responsible for the conformational and molecular recognition elements of the wrapping. Special focus is given to characterizing the nucleotide binding affinity, DNA sequence dependency, DNA length variation, SWCNT chirality, and sugar backbone (RNA vs. DNA) contributions to the wrapping conformation and SWCNT fluorescence. This article concludes with an assessment of the latest DNA-SWCNT-based sensing platforms used for the selective, single- and multi-modal detection of target analytes.