[en] The availability of high-brilliance X-ray sources, high-precision X-ray focusing optics and very efficient CCD area detectors has contributed essentially to the development of transmission X-ray microscopy (TXM) and X-ray computed tomography (XCT) with sub-50 nm resolution. Particularly, the fabrication of high aspect ratio Fresnel zone plates with zone widths approaching 15 nm has contributed to the enormous improvement in spatial resolution during the previous years. Currently, Fresnel zone plates give the ability to reach spatial resolutions of 15 to 20 nm in the soft and of about 30 to 50 nm in the hard X-ray energy range. X-ray microscopes with rotating anode X-ray sources that can be installed in an analytical lab next to a semiconductor fab have been developed recently. These unique TXM/XCT systems provide an important new capability of nondestructive 3D imaging of internal circuit structures without destructive sample preparation such as cross sectioning. These lab systems can be used for failure localization in micro- and nanoelectronic structures and devices, e.g., to visualize voids and residuals in on-chip metal interconnects without physical modification of the chip. Synchrotron radiation experiments have been used to study new processes and materials that have to be introduced into the semiconductor industry. The potential of TXM using synchrotron radiation in the soft X-ray energy range is shown for the nondestructive in situ imaging of void evolution in embedded on-chip copper interconnect structures during electromigration and for the imaging of different types of insulating thin films between the on-chip interconnects (spectromicroscopy). (orig.)