The basic point to be considered in this report is that X‐ray capillary optics relies on the ability of a tapered and/or bent capillary channel to act as an X‐ray waveguide. Recently several coherent phenomena associated with propagation of X‐rays in capillary optical elements have been observed. In order to describe coherent phenomena of radiation propagation a quantum‐wave theory of X‐ray channeling was developed. Simple estimations speak on possibility of X‐ray channeling in nano‐scale capillaries, but with a significant change in character of channeling. In this connection, discovery of carbon nanotubes opens new opportunities to apply capillary waveguide optics. X‐ray propagation in capillary micro‐ and nanostructures within the frame of wave approach will be discussed. © 2003 American Institute of Physics