The new technique of x-ray microtomography nondestructively generates three-dimensional maps of the x-ray attenuation coefficient inside small samples with approximately 1 percent accuracy and with resolution approaching 1 micrometer. Spatially resolved elemental maps can be produced with synchrotron x-ray sources by scanning samples at energies just above and below characteristic atomic absorption edges. The system consists of a high-resolution imaging x-ray detector and high-speed algorithms for tomographic image reconstruction. The design and operation of the microtomography device are described, and tomographic images that illustrate its performance with both synchrotron and laboratory x-ray sources are presented.