Continuous and eager efforts on the development of HTS materials have led their practical applications in various fields thus far. Very high Jc exceeding 1010 Am-2 at 77 K of coated conductors is now regarded as the lowest standard performance and highly reliable critical current properties of BSCCO tapes have been supporting the successful results of many research projects and development of new superconducting products. In addition, RE123 bulk materials are used for several applications, such as strong magnets, current leads, levitation systems and bearings. These suggests that critical current properties of these HTS materials are enough high against extensive practical applications. On the other hand, high production cost of HTS materials mainly due to a large number of fabrication processes to form highly grain aligned microstructure limits widespread of HTS applications. Our recent studies mainly on the effects of post-annealing at relatively high temperatures, 700~900°C, before oxygen annealing on superconducting properties of HTS indicated that precise control of nonstoichiometric cation composition is crucially important process to derive intrinsic potential of HTS. The cation composition is generally controlled by changing the starting composition, however, it unintentionally varies in the resulting materials depending on the sintering conditions, temperature, partial pressure of oxygen and external pressure. Even for Y123, which has been believed to have an exactly integral cation ratio Y:Ba:Cu=1:2:3, Y ion can substitute for Ba-site up to 2%. In the case of BSCCO, Sr-site is usually substituted by Ca and/or Bi, however, the substitution level can be controlled by applying the post-annealing process. Dramatically positive effects of precise control of cation composition near the integral ratio on superconducting properties, particularly on critical current properties, are shown for RE123, RE247 and BSCCO materials including challenges to reduce the electromagnetic anisotropy by doping and control of dopant level. Furthermore, new strategies to overcome weak-link problem at grain boundaries of HTS and the ultimate potential of HTS materials will be discussed.