For type-II superconductors, magnetic field can be trapped due to persistent internal supercurrent. Quasi-persistent magnetic fields near 2 T at 60 K (and 1.4 T at 77 K) have been measured in minimagnets made of proton-irradiated melt-textured Y-Ba-Cu-O (MT-Y123) samples. Using the trapping effect, high-field permanent magnets with dipole, quadrupole, or more complicated configurations can be made of existing MT-Y123 material, thus bypassing the need for high-temperature superconductor (HTS) wires. A phenomenological current model has been developed to account for the trapped field intensity and profile in HTS samples. This model is also a guide to select directions of materials development to further improve field trapping properties. General properties such as magnetic field intensities, spatial distributions, stabilities, and temperature dependence of trapped field are discussed.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>