The recent discovery that Nb3Sn remains superconducting in magnetic fields exceeding 88 kgauss while carrying current densities in excess of 100 000 amp/cm2has stimulated widespread activity directed toward the construction of superconducting magnets and the understanding of ``hard'' superconductivity. Some of the relevant events that have transpired since the discovery of superconductivity by Onnes in 1911 are reviewed. The critical current versus magnetic field (IcvsH) characteristics of several materials are discussed and the justification of using such measurements on small samples as a basis for magnet design is presented. Nb‐Zr alloys appear useful for magnets capable of fields as large as 80–100 kgauss while Nb3Sn appears to be useful for fields of 200 kgauss. Superconducting magnets of Nb3Sn and of Nb‐Zr have been constructed and tested by several laboratories. Fields as large as about 70 kgauss have been generated with Nb3Sn magnets and 60 kgauss with Nb‐Zr magnets. Fields exceeding 100 kgauss have been attained by augmenting the field produced by a superconducting Nb3Sn magnet with the field from a conventional Bitter solenoid. Superconducting magnets capable of fields of at least 100 kgauss are almost a certainty and it is quite likely that magnets will eventually be constructed to produce fields of 200 kgauss. Fields of several hundred kgauss are an intriguing possibility.