X-ray optical devices based on arrays of capillaries and single tapered capillaries can focus and concentrate x rays by the reflection of near-grazing-incidence rays at the interior walls of the channels. Capillary arrays are true imaging devices and can be used as focusing, condensing,and collimating optics, suitable for x-ray microcopy and astronomy. Rays which enter channels and are reflected once or twice, via total external reflection, may be redirected towards the image. Theoretical calculations of the focusing performance of arrays consisting of capillaries of square and circular cross-section are given. Experimental investigations have been made using microchannel plate (MCP) detector blanks and various x-ray sources.