Examples of concomitant ordering include magnetic ordering, Jahn-Teller cooperative ordering, electronic ordering, ionic ordering, and ordering of partially-filled sites. Concomitant ordering sets in when a crystal is cooled and always lowers the degree of symmetry of the crystal. Concomitant ordering concepts can also be productively applied to many molecules, ions, and clusters. As an educational aid, the 17 plane groups may be generated by imposing concomitant patterns on designs belonging to p4mm and p6mm, and ornamental designs may be created by applying concomitant patterns on the regular tilings. (Contains 7 figures.)