When the new YBaCuO superconductors were developed about 18 years ago, the critical maximum current density, at a magnetic field of 1.0 T and a temperature of 77 K, was still quite low. Roughly 8 years ago, it became possible to raise the critical current density to 106 A/cm2 at 1.0 T and 77 K. This opened up possibilities for application in self-stabilizing superconducting magnetic bearings and also in maglev trains capable of movement along a track. An important criterion in the high current-carrying capacity of YBaCuO superconductors is the excellent texture of melt-textured YBaCuO moldings, which must also be free of microcracks. Narrow distributions of the a-, b-, and c-axis orientations, in the absence of isotropic fractions, allow almost the entire mirror flux in the superconductor to be induced by permanent magnets.