X-ray computed tomography (CT), introduced into clinical practice in 1972, was the first of the modern slice-imaging modalities. To reconstruct images mathematically from measured data and to display and to archive them in digital form was a novelty then and is commonplace today. CT has shown a steady upward trend with respect to technology, performance and clinical use independent of predictions and expert assessments which forecast in the 1980s that it would be completely replaced by magnetic resonance imaging. CT not only survived but exhibited a true renaissance due to the introduction of spiral scanning which meant the transition from slice-by-slice imaging to true volume imaging. Complemented by the introduction of array detector technology in the 1990s, CT today allows imaging of whole organs or the whole body in 5 to 20 s with sub-millimetre isotropic resolution. This review of CT will proceed in chronological order focussing on technology, image quality and clinical applications. In its final part it will also briefly allude to novel uses of CT such as dual-source CT, C-arm flat-panel-detector CT and micro-CT. At present CT possibly exhibits a higher innovation rate than ever before. In consequence the topical and most recent developments will receive the greatest attention.