The present paper reviews the computed tomography imaging spectrometer (CTIS) measurement systems at home and abroad from the aspects of technological characterizations and research focuses. The developments of computed tomography imaging spectrometers are described, involving the adding new abilities by improving systematic structure and by incorporating other elements or systems, the study and applications of novel grating elements, detectors or apparatus, the optimizations and improvements of the system calibration methods and reconstruction algorithms. In addition, based on the classification of application scope, the extension status of probing spectral bands and application fields towards computed tomography imaging spectrometers and related systems are summarized. The principles of non-scanning computed tomography imaging spectrometer and high-throughput computed tomography imaging spectrometer are introduced. Moreover, the trends of computed tomography imaging spectrometers are discussed too.