In x-ray computed tomography (CT), materials with different elemental compositions can have identical CT number values, depending on the mass density of each material and the energy of the detected x-ray beam. Differentiating and classifying different tissue types and contrast agents can thus be extremely challenging. In multienergy CT, one or more additional attenuation measurements are obtained at a second, third or more energy. This allows the differentiation of at least two materials. Commercial dual-energy CT systems (only two energy measurements) are now available either using sequential acquisitions of low-and high-tube potential scans, fast tube-potential switching, beam filtration combined with spiral scanning, dual-source, or dual-layer detector approaches. The use of energy-resolving, photon-counting detectors is now being evaluated on research systems. Irrespective of the technological approach to data acquisition, all commercial multienergy CT systems circa 2020 provide dual-energy data. Material decomposition algorithms are then used to identify specific materials according to their effective atomic number and/or to quantitate mass density. These algorithms are applied to either projection or image data. Since 2006, a number of clinical applications have been developed for commercial release, including those that automatically (a) remove the calcium signal from bony anatomy and/or calcified plaque; (b) create iodine concentration maps from contrast-enhanced CT data and/or quantify absolute iodine concentration; (c) create virtual noncontrast-enhanced images from contrast-enhanced scans; (d) identify perfused blood volume in lung parenchyma or the myocardium; and (e) characterize materials according to their elemental compositions, which can allow in vivo differentiation between uric-acid and non-uric-acid urinary stones or uric acid (gout) or non-uric-acid (calcium pyrophosphate) deposits in articulating joints and surrounding tissues. In this report, the underlying physical principles of multienergy CT are reviewed and each of the current technical approaches are described. In addition, current and evolving clinical applications are introduced. Finally, the impact of multienergy CT technology on patient radiation dose is summarized.