The steadily increasing magnetic fields that can be generated with superconducting magnets are reaching the limits of what is achievable with low-temperature superconductors (LTS). At the same time, a reduction of fossil-fuel extraction will amplify the already limited availability of helium as a coolant for superconducting magnets in the near future. Hence, manufacturers of commercial applications that rely on superconducting magnets have become increasingly interested in exploring technologies that enable a move beyond the magnetic-field limitations posed by LTS conductors, and/or enable higher operating temperatures to allow for cryogen-free operation. High-temperature superconductors (HTS), such as REBCO, Bi-2212, and Bi-2223 have all matured to a certain commercial extent, and have thereby become enablers for such technologies. The emergence of various new commercial magnet-systems that utilize HTS, suggests that we are at the dawn of a wider commercial implementation. A review of which HTS properties are critical for these magnets, what is currently available, and what is missing, is therefore considered timely and appropriate in this context.