Single-walled carbon nanotubes (SWNTs) are a fundamental family of distinct molecules, each bearing the possibility of different reactivities due to their intrinsically distinct chemical properties. SWNT syntheses generate a heterogeneous mixture of species with varying electronic character, lengths, diameters and helicities, (n,m), as well as other amorphous, graphitic and metal catalyst impurities. In recent years, selective syntheses and post-synthetic separation strategies have advanced, driven by the requirement for pure SWNTs displaying particular features. Covalent surface modifications are widely-used to adapt SWNTs for specific applications with modified solubility, compatibility and specific functionalities. In many cases, such reactions have been found to be selective, illuminating the fundamentally distinct chemistry of each (n,m) species. This differential reactivity has found immediate utility in facilitating the sorting of nanotubes according to specific diameter, electronic properties and, most importantly, helicity. In this tutorial review, we discuss a wide range of selective reactions, the mechanisms that are thought to govern selectivity, and the challenges of separating, characterising and regenerating the modified SWNTs.