Understanding of the mechanism of current-induced magnetic domain wall (DW) motion is essential for practical use of this phenomenon. Recent experiment has revealed that in perpendicularly magnetized Co/Ni nano-wire the threshold current density for DW motion is determined by 'intrinsic pinning' and it is independent of the DW pinning strength. Besides, the velocity of DW motion has been shown to be independent of external magnetic fields. In this review, recent progress of the study on the current-induced DW motion is described.