We review the current X-ray techniques with 3D imaging capability at the nano-scale: transmission X-ray microscopy, ptychography and in-line phase nano-tomography. We further review the different ultra-structural features that have so far been resolved: the lacuno-canalicular network, collagen orientation, nano-scale mineralization and their use as basis for mechanical simulations. X-ray computed tomography at the micro-metric scale is increasingly considered as the reference technique in imaging of bone micro-structure. The trend has been to push towards increasingly higher resolution. Due to the difficulty of realizing optics in the hard X-ray regime, the magnification has mainly been due to the use of visible light optics and indirect detection of the X-rays, which limits the attainable resolution with respect to the wavelength of the visible light used in detection. Recent developments in X-ray optics and instrumentation have allowed to implement several types of methods that achieve imaging that is limited in resolution by the X-ray wavelength, thus enabling computed tomography at the nano-scale. We review here the X-ray techniques with 3D imaging capability at the nano-scale: transmission X-ray microscopy, ptychography and in-line phase nano-tomography. Further, we review the different ultra-structural features that have so far been resolved and the applications that have been reported: imaging of the lacuno-canalicular network, direct analysis of collagen orientation, analysis of mineralization on the nano-scale and use of 3D images at the nano-scale to drive mechanical simulations. Finally, we discuss the issue of going beyond qualitative description to quantification of ultra-structural features.