This article gives a topical review of the application of the scanning tunnelling microscope ( STM) to the characterisation of thin films ( typically monolayers) of organic molecules on surfaces. Three classes of molecules are considered: self- assembled thiol monolayers, macrocycles, e. g. porphyrins and cyclophanes, and passivated nanoparticles. Typically these molecules are deposited onto the surface of, e. g. gold/ graphite, from a solution. The STM is shown to be a tool not just for imaging, from the morphology of the film down to the level of individual molecules, but also for molecular manipulation and for electrical measurements. Indeed, an appropriate understanding of the electrical characteristics of the STM measurement is essential for successful imaging of organic ( or biological) molecules.