X-ray tomographic microscopy (XTM), utilizing intense, highly collimated synchrotron radiation, has been used to nondestructively image materials structures in three dimensions. The spatial resolution of the technique approaches that of conventional optical microscopy, but XTM does not require polished surfaces or serial sections. We present the results of an XTM investigation of a composite material composed of silicon-carbide fibers in an aluminum matrix. The results reveal the aluminum/silicon-carbide interfaces and show microcracks running along many of the interfaces as well as in the matrix. Excellent contrast is observed between the silicon-carbide sheath of the fiber surrounding the graphite core and the coating at the fiber-matrix interface. The sensitivity to small changes in the linear absorption coefficient allows nondestructive imaging of variations in chemistry between graphite and silicon carbide and between silicon carbide and aluminum. The experimentally determined values of the absorption coefficients of these phases are identical to values published in the literature. For the first time, XTM will allow observation of damage accumulation and crack growth during deformation testing. The availability of such data will greatly improve our understanding of failure in advanced materials.