Superconductivity for Magnets

The present state of development of a series of industrial superconductors is reviewed in consideration of their future applications in high field accelerator magnets, with particular attention on the material aspect. The discussion is centred on Nb$_{3}$Sn and MgB2, which are industrially available in a round wire configuration in kilometre lengths and are already envisaged for use in the LHC Upgrade (HL-LHC). The two systems Bi-2212 and R.E.123 may be used in magnets with even higher fields in future accelerators: they are briefly described.