Ornament was one of the key concepts in the nineteenth century discussions on architecture and decorative arts. In the beginning of the twentieth century, modernism abandoned ornament from its vocabulary. In the last decades of the twentieth century, the heritage of Modernism and its rejection of ornament were critically analyzed and ornament became a topical subject once more. Geometry played an important role in the search for rational and intellectual basis for the architecture and decorative arts in the beginning of industrial age. Arabic ornamental practice with its geometrical foundation served as one precept in searching and formulating appropriate design principles for architecture and decorative arts in the nineteenth century. In Arabic ornamental design different geometrical grids function as a starting point which offers unlimited possibilities for designs. In the twentieth century, the Western aesthetics limited to the simple grid formed by horizontal and vertical lines. This chapter reflects on the history and the heritage of the ornament discussions focusing especially on the role of geometrics in the conceptions of ornament.