The commercially available high temperature superconductors (HTS) tapes and wires (BSSCO and REBCO) are introduced and the past and present projects to build fusion devices using HTS based magnets are reviewed. The main design options for high current, high field conductors are presented with the related R&D and the open issues. Depending on the material, the cable layout and the application specific needs, the challenges for HTS magnet technology are different, ranging from the anisotropic properties of the REBCO tapes, to the large volume heat treatment under high pressure for Bi-2212, to the ability to withstand the large transverse loads, to the optimization of the electrical connections for segmented coil assembly, to the ambitious target of fully demountable TF coils for tokamaks. For the generation of magnetic fields larger than 18–20 T, the HTS represents the enabling technology. The use of the expensive HTS can be better justified for applications, which are out of range for conventional, low temperature superconductors (LTS). Eventually, a roadmap for future R&D is sketched focusing on medium term technology milestones, e.g. addressing the issue of quench protection in HTS large magnets, the industrial manufacture of robust high current HTS cables and the engineering design/demonstration of demountable winding packs.