This paper briefly reviews how scanning tunnelling microscopy (STM) and spectroscopy (STS) are used to analyse the atomic structure and the electronic properties of individual single-wall carbon nanotubes. In this area, the progress accomplished over the past several years has been spectacular. As this paper demonstrates, all the effects predicted by theory have been verified experimentally. Geometrical and electronic effects specific to carbon nanotubes are illustrated by analysing a series of STM images and STS spectra computed using a tight-binding theory. The simulations include a catalogue of images of 27 single-wall nanotubes, Stone-Wales defects in semiconducting nanotubes, and a symmetric Y-junction.