High-field, low-inductance superconducting magnets in particle accelerators and fusion machines require high operating currents, often in combination with high current densities and for some applications conductor bending radii of less than 50 mm. These requirements form a major challenge for magnet conductors consisting of high-temperature superconductors, which are required for reaching magnetic fields exceeding 20 T, or allowing for operating temperatures above 20 K. The high tolerance of RE-Ba 2 Cu 3 O 7−δ coated conductors to axial tensile and compressive strain has led to the concept of CORC ® cables in an attempt to develop a round and mechanically as well as electrically isotropic, high-performance conductor that would meet these challenging requirements. This review article will outline how CORC ® cables evolved from a concept into a practical and robust conductor for high-field magnets and compact superconducting power cables. This review article provides an extensive overview of how CORC ® cable technology has overcome most of the challenges associated with its use in large magnets for fusion, particle accelerators and in helium gas cooled power and fault current limiting cables, while further development is ongoing that will push the CORC ® cable technology to even higher performance levels.