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Recording of Manuel Guizar-Sicairos' (Paul Scherrer Insitut) talk on September 30, 2021, at the EPFL Seminar Series in Imaging. Abstract. Access to local information about material composition and its 3D distribution at the nanoscale is of chief importance for studying functional hierarchical materials, for example in biology, materials science, and energy research. The small wavelength of X-rays offers the opportunity to image with very high resolution.This property combined with the high-penetration of photons, with energies on the order of multiple keV, are ideal for nanoscale-resolution imaging in a minimally intrusive, i.e. non-destructive, procedure. In this talk I will discuss principles, applications, and latest advances on two techniques that we develop to probe nanostructure: ptychographic X-ray nanotomography (PXCT) and small-angle scattering tensor tomography (SASTT). PXCT is a coherent lensless imaging technique that circumvents the difficulties of fabricating X-ray lenses of sufficient resolution by replacing the imaging lens with iterative phase-retrieval algorithms. Currently it achieves a resolution of 15 nm in 3D in volumes of thousands of cubic microns and 100 nm in volumes of a million cubic microns. SASTT, highly complementary to PXCT, is capable of quick surveys of average local 3D nanostructure anisotropy. SASTT bridges and correlates information from nano (1 – 200 nm) and macroscopic (1 – 10 mm) length scales. Examples from a number of areas will be presented including integrated circuits, neuroscience, and energy research. Latest results leveraging sparsity to combine PXCT with spectroscopy for structural and functional nanoscale characterization will also be discussed. Slides illustrations video: https://go.epfl.ch/Guizar See upcoming talks on: imagingseminars.org The EPFL Seminar Series in Imaging is run by EPFL Center for Imaging: imaging.epfl.ch