Single-walled carbon nanotubes (SWCNTs) have attracted great attention on account of their superior and tunable electrical properties for promising applications in low-cost and high-performance nano-electronics and thin-film devices. However, SWCNTs are usually produced as a mixture of m-/s-nanotubes with small diameters and long aspect ratios and tend to form bundles or entangled ropes owing to their high van der Waals attraction and p-p interactions among their inter-tubes. Therefore, the dispersion and sorting of SWCNTs with both a high yield and desirable electronic structures has been a great challenge but a long-term motivation to achieve greater practical utility of SWCNTs. This review provides a comprehensive summary of the strategies for the surface modification and dispersion of SWCNTs, and surveys progress on the up-to-date development of SWCNTs enrichment via mainly non-covalent interactions with molecular species. The effect of the molecular architecture on the selective dispersion and sorting of SWCNTs by surfactants, bio-macromolecules, and conjugated polymers is discussed with respect to the structure-property relationship and interaction mechanism.