There are over 5000 superconducting materials but only about 5 have ever been useful for applications in magnets, while HEP, which has been so vital for the development of superconducting magnet technology has made virtually every magnet out of just one, the simple bcc alloy Nb-Ti with Tc of 9 K and upper critical field ~ 14T (at 2K). Significant demonstrations of the capability of the brittle intermetallic Nb3Sn have shown that fields of more than 15 T can be generated in dipole form. But Nb-Ti and Nb3Sn are staid, conventional superconductors, far from the cutting edge of superconducting science research where cuprates like YBa2Cu3O7-x and Bi2Sr2CaCu2Ox remain at the scientific forefront and in 2008 were joined by the recently discovered Fe-As pnictide superconductors. What could it mean to have materials for magnets with 10 times the Tc of Nb-Ti (90-120 K) and 3 or more times the critical field (100-240 T)? One enormous barrier is that higher Tc so far always means more complexity and a more localized superconducting interaction which is sensitive to local loss of superconductivity. The issue that has made the cuprate high temperature superconductors so hard to apply is that grain boundaries which form a 3D network in any practical wire form, easily acquire degraded superconducting properties. But conductors can now be made with extreme texture so that grain boundaries are minimized. Moreover almost practical conductors of Bi2Sr2CaCu2Ox and YBa2Cu3O7-x are now are in production and in late 2008 we were, at the Magnet Lab, able to make small solenoids operating at high current density in fields of 32 and almost 34 T respectively. Within the HEP community, there is enthusiasm to embrace HTS conductors for new very high field machines that could, like the Muon Collider, use fields of 30-50 T. In my talk I would like to explore the underlying science controlling such potential applications.