This paper describes a tunable X-ray focusing apparatus, referred to as a transfocator, based on compound refractive lenses. By varying the number of lenses in the beam, the X-ray energy focused and the focal length can be varied continuously throughout a large range of energies and distances. The instrument can be used in both white and monochromatic beams to focus, pre-focus or collimate the beam. The transfocator can be used with other monochromators and/or other focusing elements, leading to significant increases in flux. Furthermore, the chromatic nature of the focusing means the transfocator suppresses harmonics and can also be used as an extremely high flux broad-band-pass monochromator. These devices have been installed in the first optics and second experimental hutches at the ID11 beamline at the ESRF.