This chapter presents the principle of X-ray CT and its evolution during the last 40 years. The first section describes the physical basis of X-ray CT, tomographic image reconstruction algorithms, and the source of artifacts in X-ray CT images. The second section is devoted to the evolution of CT technology from the first translation-rotation systems to multi-slice spiral CTs currently used today. The next section addresses specific developments of CT technology and applications, like perfusion CT, quantitative CT, and spectral CT. The fourth section introduces the problem of radiation exposure delivered to the patient and its evaluation. Finally the last section addresses the development in micro- and even nano-CT which is a rapidly evolving area in preclinical imaging and biology.