Higher efficiency, lower cost refrigeration is needed for both large and small scale cooling. Refrigerators using entropy changes during cycles of stretching or hydrostatically compression of a solid are possible alternatives to the vapor-compression fridges found in homes. We show that high cooling results from twist changes for twisted, coiled, or supercoiled fibers, including those of natural rubber, NiTi, and polyethylene fishing line. By using opposite chiralities of twist and coiling, supercoiled natural rubber fibers and coiled fishing line fibers result that cool when stretched. A demonstrated twist-based device for cooling flowing water provides a high cooling energy and device efficiency. Theory describes the axial and spring index dependencies of twist-enhanced cooling and its origin in a phase transformation for polyethylene fibers.