Since carbon nanotubes (CNTs) display unique structures and remarkable physical properties, a variety of applications have emerged in both materials and life sciences. In terms of applications, the functionalisation of nanotubes is extremely important, as it increases their solubility and processability, and combines the unique properties of single-walled carbon nanotubes (SWCNTs) with those of other classes of materials. A number of methods have been developed, which can be divided into two major approaches: (1) non-covalent supramolecular modifications, and (2) covalent functionalisation. In this tutorial review, we survey the covalent modification of SWCNTs with organic moieties, and illustrate the major analytical techniques routinely used to characterise the functionalised materials.