Abstract—Recently, the number of projects has grown connected with the application of high-temperature superconductors (HTSC) with exceptionally high current-carrying characteristics in strong magnetic fields. However, the thickness of the RBa2Cu3O7–x (R = REE, Y) superconducting layer is only 1–2% of the thickness of HTSC tape. Increasing the current-carrying characteristics owing to the thickness of the conducting layer is a promising approach. The fundamental problem of crystallite formation of a-oriented crystallites prevents the development of this approach. Such crystallites do not carry superconducting current along the substrate tape and interfere with the growth of c-oriented crystallites. This review presents existing methods of suppression of a-oriented growth, the basis of the creation of HTSC materials, and prospects of obtaining HTSC materials with high current-carrying characteristics.