REBa2Cu3O7-δ (REBCO, RE: rare earth elements) superconductors have been considered as the candidate for electric power industries such as power cable and high magnet coil application, because of their high critical current with zero resistance at temperature beyond liquid nitrogen temperature. REBCO wires consisted of superconducting thin films with highly crystal grain alignment and high critical current density in high external magnetic fields are required for the electric power applications. In this report, the growth techniques for REBCO superconductor single crystals and REBCO thin films are described. The Solute-Rich-Liquid Crystal Pulling (SRL-CP) method is a good technique for the fabrication of high quality large REBCO single crystals. The REBCO single crystals grown by this method have been applied to the scientific materials characterization. On the other hand, highly oriented REBCO thin films have been fabricated using a metal organic deposition (MOD) technique. Flux pinning centers are introduced artificially into the films through MOD process to enhance critical current density in magnetic fields.