We describe refractive x-ray lenses with a parabolic profile that are genuine imaging devices, similar to glass lenses for visible light. They open considerable possibilities in x-ray microscopy, tomography, microanalysis, and coherent scattering. Based on these lenses a microscope for hard x rays is described, that can operate in the range from 2 to 50 keV, allowing for magnifications up to 50. At present, it is possible to image an area of about 300 μm in diameter with a resolving power of 0.3 μm that can be increased to 0.1 μm. This microscope is especially suited for opaque samples, up to 1 cm in thickness, which do not tolerate sample preparation, like many biological and soil specimens. © 1999 American Institute of Physics.