Superconducting magnets used in applications such as magnetic resonance imaging (MRI) and nuclear magnetic resonance (NMR) require significant temporal magnetic field stability, which can be achieved when the MRI and NMR magnets are operated in the persistent current mode (persistent-mode) using superconducting joints. However, the ultra-high field MRI and NMR magnets are sometimes operated in the driven mode. Herein, we present an analysis of the temporal magnetic field drift and fluctuations observed for MRI and NMR magnets operating in the driven mode and an exploration of effective methods for stabilizing the temporal magnetic field fluctuations. In the last decade, substantial improvements have been achieved in superconducting joints between high-temperature superconductors (HTS). These superconducting joints enable the development of persistent-mode ultra-high field magnets using HTS coils. Therefore, we herein review the superconducting joint technology for HTS conductors and describe the results of the persistent-mode operation achieved by a medium-field NMR magnet using an HTS coil. Particularly, the cutting-edge progress achieved concerning HTS superconducting joints, including joining methods, superconducting properties, and future prospects, is highlighted along with the issues that need to be addressed.