In this paper we describe the application of a new high-resolution X-ray tomographic microscope to the study of porous media. The microscope was designed to exploit the properties of a synchrotron X-ray source to perform three dimensional tomography on millimeter sized objects with micron resolution and has been used in materials science studies with both synchrotron and conventional x-ray sources. An overview of the microscope design, operating modes, the reconstruction algorithm and the data display will be presented. The performance of the microscope using conventional and synchrotron sources will be compared. In this work we have applied the microscope to measure the three dimensional structure of fused bead packs and berea sandstones with micron resolution and have performed preliminary studies of flow in these media with the microscope operated in a digital subtraction radiography mode. Computer graphics techniques have been applied to the data to visually display the structure of the pore body system. Tomographic imaging after flow experiments should detect the structure of the oil-water interface in the pore network and this work is ongoing.