Nematics are materials that have only orientation order, usually described by a non-zero, uniaxial average for a traceless symmetric second rank tensor. I review our knowledge about orientational order involving a single traceless symmetric second rank tensor order parameter or a single vector order parameter. There is recent interest in systems with either higher rank tensor order parameters or additional important, possibly higher rank orientational order parameters. I will discuss theoretical results for such generalized nematics, including the rather striking differences between systems with single low rank tensor and single high rank tensor order parameters. Such differences, which seem to be generic to high-rank tensor order parameters in various symmetry groups, may help to explain the GUTS / Electroweak phase transition in high energy theory as well as phenomena in condensed matter physics.