Since Röntgen discovered x-rays at the end of the nineteenth century and established their usefulness for medical diagnostics imaging, many technological advances have allowed for x-rays to be employed in even more powerful ways. This includes utilizing x-rays for tomographic imaging and quantification. This chapter describes the principles of microcomputed tomography (microCT) and its use in obtaining internal structural and compositional data about materials/objects of interest. The authors introduce this material with a brief history of the development of laboratory and synchrotron microCT for engineering, biology, and biomedical applications. As will be evident, microCT imaging requires many components to operate together with precision, and the standard microCT subsystems will be described. This chapter will also explain the principles behind x-ray attenuation in materials as well as common methods by which microCT image processing software may handle complex detected data to reconstruct grayscale slice images. The quality of the resulting images relies on a few key factors, including spatial resolution, noise, and contrast, and these concepts will be explained. Additionally, microCT image reconstruction and processing may produce various types of artifacts, and the most common of these artifacts will be discussed. In a typical microCT imaging workflow, the reconstructed two-dimensional (3-D) slice images can subsequently be processed to generate segmentations and three-dimensional (3-D) renderings of the material(s) of interest. Because image segmentation and quantification of the material's geometry and composition could be performed via many possible procedures, these processes will be generally discussed within this chapter. Finally, microCT forms the basis for various novel techniques that are rapidly gaining momentum for use in biology, engineering, and biomedical research applications to provide accurate, non-destructive high-resolution images and quantitative data. Some of these techniques, such as phase contrast CT, dual-energy CT, fluorescence CT, and x-ray scattering tomography, will be introduced and briefly discussed.