A compact laboratory x-ray "nano-CT" scanner has been created for 3D non-invasive imaging with 150-200 nanometers 3D spatial resolution, using advanced x-ray technologies and specific physical phenomena for signal detection. This spatial resolution in volume terms is 3 orders better than can be achieved in synchrotron tomography, 5 orders better then in existing laboratory micro-CT instruments and 10-12 orders better in comparison to clinical CT. The instrument employs an x-ray source with a 300-400nm x-ray spot size and uses small-angle scattering to attain a detail detectability of 150-200nm. An object manipulator allows positioning and rotation with an accuracy of 150nm. The x-ray detector is based on an intensified CCD with single-photon sensitivity. A typical acquisition cycle for 3D reconstruction of the full object volume takes from 10 to 60 minutes, with the collection of several hundred angular views. Subsequent volumetric reconstruction produces results as a set of cross sections with isotropic voxel size down to 140 x 140 x 140nm, or as a 3D-model, which can be virtually manipulated and measured. This unique spatial resolution in non-invasive investigations gives previously unattainable 3D images in several application areas, such as composite materials, paper and wood microstructure, biomedical applications and others.