Maps with coloured relief shading, modulated by elevation and by exposure to illumination, present topography in a particularly vivid and descriptive manner. Carefully modulated illumination and shading shown in continuous colour tones simulate the third dimension of topography, helping map-readers to conceive more easily the terrain's important landforms. Since the end of the 19th century, cartographers have developed a wide variety of colour schemes. The first part of this paper illustrates the graphical and technical developments of the past, leading to Swiss-style coloured relief shading; the second part presents a new computer-based method for colourizing grey-shaded relief inspired by classic colour schemes. The method uses a colour look-up table and a digital elevation model. The colour look-up table has colours for all combinations of initial grey values and terrain elevations. It is constructed from interactively placed colour reference points.