Advances on permanent high-T(c) superconducting magnets are reported. Materials are tested in the form of small tiles. An accurate phenomenological model of the currents in a magnetized tile predicts that the maximum trapped field B(T,max) is-proportional-to J(c)f(d), where J(c) is the critical current density, d is the diameter of the single-grain tile, and f(d) is a function which increases monotonically with d. Results are reported of increasing J(c) via chemical additives, and via bombardment by high-energy light ions and fission fragments. Increases in d via chemical and temperature gradients are also reported. Methods, data, and most recent results are presented. Present values are d = 2 cm, and J(c) = 85 kA/cm2, at 77 K. A six tile minimagnet, 1.2 X 1.2 X 1.5 cm3, fabricated from earlier tiles with d approximately 1 cm, J(c) approximately 45 kA/cm2, retains 1.52 T at 77 K. It is calculated that the more recent values of J(c) and d will result in fields of 3 T at 77 K. B(T,max) also increases rapidly with T-1, and approximately doubles at 60 K.