The current status of large-grained RE-Ba-Cu-O (RE: Y or rare earth elements) bulk superconductors with excellent superconducting properties is described. Gd-Ba-Cu-O bulk superconductors can trap a very high magnetic field even if they are melt-processed in air. Although the electromagnetic force caused by the trapped field is larger for a larger sample and may break the sample, a large sample of Gd-Ba-Cu-O 46 mm in diameter has the potential of trapped magnetic fields greater than 10 T at around 40 K. In addition, single-grained bulk superconductors as large as 150 mm can be obtained using the RE compositional gradient method. Dy-Ba-Cu-O is an ideal material for current leads because it has low thermal conductivity and high critical current density at 77 K in high magnetic fields. Eu-Ba-Cu-O has low magnetic permeability, and is therefore suitable for bulk NMR applications. Progress in machining technology has made possible various bulk superconductors with complicated shapes such as coils, leading to small and strong electromagnets by stacking several coil-shaped bulk superconductors together.