Progress in nanoscience and nanotechnology depends not only on examining the surfaces of nanostructures but on looking deep inside to identify what electronic, magnetic, optical, and chemical processes are of importance. For characterizing internal variations in shape, organization, or chemical composition over distances of hundred of nanometers, usage of XUV and soft X-ray electromagnetic radiation not only complements electron microscopy but also offers important advantages. Unfortunately the relevant sources in this spectral region (Synchrotrons and Free Electron Lasers) are extremely large, prohibitedly expensive, and not accessible to most of the scientific community. We propose to use XUV and soft X-rays produced by High Harmonic Generation (HHG), as the source for exploring most advanced multidimensional (3D spatial+1D frequency+1D time) imaging modalities for nanostructures and nanomaterials, and studying their fundamental physical properties and dynamics. Specifically, we propose to research the combination of multicolor nano-tomography and optical coherence tomography with high harmonic generated light, making particular emphasis on three-dimensional volumetric structural and property analysis. We will also use the HHG to study fundamental optical properties of nano-materials in XUV and soft X-ray region of spectrum - very important and largely unexplored area so far. We believe that such an interdisciplinary approach (attoscience techniques applied into nanoscience) can result in qualitatively new advances in the field.