Persistent current joints are crucial components of superconducting magnets—enabling the production of the high and ultra-stable magnetic fields required, for instance, for magnetic resonance measurements. At this critical juncture when persistent mode magnets containing commercial high temperature superconductors may soon become a reality, it is of value to take stock and evaluate current challenges faced in the field of jointing. This paper provides a review of progress made to date on the production and characterization of joints between the five major technological superconductors—NbTi, Nb3Sn, MgB2, BiSCCO and REBCO, including the materials that are used to make these joints.