Hard x-ray full field and scanning microscopy both greatly benefit from recent advances in x-ray optics. In full field microscopy, for instance, rotationally parabolic refractive x-ray lenses can be used as objective lens in a hard x-ray microscope, magnifying an object onto a detector free of distortion. Using beryllium as lens material, a hard x-ray optical resolution of about 100 nm has been obtained in a field of view of more than 500 micrometers. Further improvement of the spatial resolution to below 50 nm is expected. By reconstructing the sample from a series of micrographs recorded from different perspectives, tomographic imaging with a resolution well below one micrometer was achieved. The technique is demonstrated using a microchip as test sample. In scanning microscopy and tomography, the sample is scanned through a hard x-ray microbeam. Different hard x-ray analytical techniques can be exploited as contrast mechanism, such as x-ray fluorescence, absorption, or scattering. In tomographic scanning mode, they yield for example local elemental, chemical, or structural information from inside a specimen. At synchrotron radiation sources, a small and intensive microbeam can be generated by imaging the source onto the sample position in a strongly reducing geometry, e.g., by parabolic refractive x-ray lenses. With nanofocusing refractive x-ray lenses, a lateral beam size of 50 nm was reached. As an example for scanning tomography, we consider tomographic small angle x-ray scattering (SAXS-tomography), reconstructing a series of SAXS patterns related to small volume elements inside a polymer rod made by injection moulding.