Single-walled carbon nanotubes (SWCNTs) have attracted significant attention due to their outstanding mechanical, chemical and optoelectronic properties, which makes them promising candidates for use in a wide range of applications. However, as-produced SWCNTs have a wide distribution of various chiral species with different properties (i.e. electronic structures). In order to take full advantage of SWCNT properties, highly purified and well-separated SWCNTs are of great importance. Recent advances have focused on developing new strategies to effectively separate nanotubes into single-chirality and/or semiconducting/metallic species and integrating them into different applications. This review highlights recent progress in this cutting-edge research area alongside the enormous development of their identification and structural characterization techniques. A comprehensive review of advances in both controlled synthesis and post-synthesis separation methods of SWCNTs are presented. The relationship between the unique structure of SWCNTs and their intrinsic properties is also discussed. Finally, important future directions for the development of sorting and purification protocols for SWCNTs are provided.