The sources and structures of dyes used to colour Western historical textiles are described in this tutorial review. Most blue and purple colours were derived from indigo--obtained either from woad or from the indigo plant--though some other sources (e.g. shellfish and lichens) were used. Reds were often anthraquinone derivatives obtained from plants or insects. Yellows were almost always flavonoid derivatives obtained from a variety of plant species. Most other colours were produced by over-dyeing--e.g. greens were obtained by over-dyeing a blue with a yellow dye. Direct analysis of dyes isolated from artefacts allows comparison with the historical record.