The orientation distribution or texture of the crystallites is one of the most important structural parameters of polycrystalline materials. Texture studies were carried out for more than fifty years. This branch of materials science, first established by G. Wassermann in 1939 by his monograph “Texturen metallischer Werkstoffe,” has now developed into a quantitative science based mainly on measurements by X-ray, neutron and electron diffraction. A mathematical theory of textures has evolved mainly in the last twenty years. The extension of interest from basic metals to all kinds of crystalline materials is one of the present features. Concludingly, the future development in the field of textures may be extrapolated.