Existence of interference structures at the focal spot of regular x-ray capillary lenses and poles is discovered experimentally by our group. This effect was investigated by means of synchrotron and x-ray tube. We point out the possibility of use for capillaries twisting for control of polarizable characteristics, e.g., for rotation of a polarization plane of x ray, neutron radiation, etc. The possibility of radiation monochromatization on the level (lambda) /(Delta) (lambda) approximately equals 103 by means of a lens is also shown. Features of image transfer using interference effects in capillary structures were investigated. General wave theory of these effects is proposed. A number of important applications based on the higher illumination of x-ray lenses as compared with zone plates are considered.