Synchrotron-based X-ray Tomographic Microscopy (SRXTM) is nowadays a powerful technique for non-destructive, high-resolution investigations of a broad kind of materials. High-brilliance and high-coherence third generation synchrotron radiation facilities allow micrometer and sub-micrometer, quantitative, three-dimensional imaging within very short time and extend the traditional absorption imaging technique to edge-enhanced and phase-sensitive measurements. At the Swiss Light Source TOMCAT, a new beamline for TOmographic Microscopy and Coherent rAdiology experimenTs, has been recently built and started regular user operation in June 2006. The new beamline get photons from a 2.9 T superbend with a critical energy of 11.1 keV. This makes energies above 20 keV easily accessible. To guarantee the best beam quality (stability and homogeneity), the number of optical elements has been kept to a minimum. A Double Crystal Multilayer Monochromator (DCMM) covers an energy range between 8 and 45 keV with a bandwidth of a few percent down to 10-4. The beamline can also be operated in white-beam mode, providing the ideal conditions for real-time coherent radiology. This article presents the beamline design, its optical components and the endstation. It further illustrates two recently developed phase contrast techniques and finally gives an overview of recent research topics which make intense use of SRXTM.