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High-field superconducting solenoids have proven themselves to be of great value to scientific research in a number of fields, including chemistry, physics and biology. Present-day magnets take advantage of the high-field properties of Nb3Sn, but the high-field limits of this conductor are nearly reached and so a new conductor and magnet technology is necessary for superconducting magnets beyond 25 T. Twenty years after the initial discovery of superconductivity at high temperatures in complex oxides, a number of high temperature superconductor (HTS) based conductors are available in sufficient lengths to develop high-field superconducting magnets. In this paper, present day HTS conductor and magnet technologies are discussed. HTS conductors have demonstrated the ability to carry very large critical current densities at magnetic fields of 45 T, and two insert coil demonstrations have surpassed the 25 T barrier. There are, however, many challenges to the implementation of HTS conductors in high-field magnets, including coil manufacturing, electromechanical behavior and quench protection. These issues are discussed and a view to the future is provided.