Low temperature superconductors like Nb-Ti and Nb3Sn have enabled virtually all of today’s superconducting magnets including machines like the Large Hadron Collider with 8 T Nb-Ti dipole magnets and 1 GHz NMR spectrometers with 23 T field supplied by hybrid Nb-Ti/Nb3Sn magnets, presently the highest field all-superconducting user magnet. A recent NRC report  has described the scientific and technology rationales for many new types of ultra-high field superconducting magnet: regional 32 T superconducting magnets, a 40 T superconducting magnet, 28 – 37 T high-resolution NMR superconducting magnets, 25 – 40 T for x-rays and neutrons, 60 T DC, 20 T for human MRI, as well as magnets for fusion, particle-accelerators, radiotherapy, axion and other particle detectors. The materials and magnet technology have now made sufficient progress that a few of these magnets are now feasible. I will describe this progress and the various pluses and minuses of the three present high-temperature superconductor types and suggest some timelines under which high field coils beyond the capabilities of present-day Nb-Ti and Nb3Sn magnets might start to make it into commercial fabrication. At the NHMFL we have shown that High Temperature Cuprate Superconductors can generate test coils with fields of 45 T, almost twice the Nb-based superconductor limit and now equal to the world record 45 T DC field of the NHMFL User Magnet which requires 28 MW of DC power and a large 11 T Nb3Sn superconducting outsert magnet.
*Work carried out with many collaborators at the MagLab, especially with programs led by Huub Weijers, Denis Markiewicz (32 T), Ulf Trociewitz (Bi-2212 coils), Seungyong Hahn (NI REBCO), Scott Marshall (Bi-2223), Eric Hellstrom, Jianyi Jiang, and Fumitake Kametani (Bi-2212 conductors), and Dmytro Abraimov and Jan Jaroszynski REBCO conductors.
 B. I. Halperin BI et al., High magnetic field science and its application in the United States: Current status and future directions. Washington, D.C.: The National Academies Press, 2013. http://www.nap.edu/catalog/11211/opportunities-in-high-magnetic-field-science.