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Interest in single photon emission computed tomography (SPECT) has been renewed as a result of the successful application of transmission (x-ray) CT to diagnostic radiology. Many aspects of SPECT are different from those encountered in transmission CT, and often are more difficult to overcome. Examples of two major aspects encountered are 1) the limitations on the available photon flux imposed mainly by dose considerations to the patient and, 2) the internal attenuation of gamma rays within the patient prior to detection. Progress has been made recently in overcoming the quantum limitation by designing SPECT systems using special collimation and large active detector areas. High efficiency systems have been designed and built using both multiple-scanners and also using multiple large-field-of-view scintillation cameras. Much progress has also been made in compensating for the problem of gamma ray attenuation using iterative and analytical approaches. This paper reviews the history of single photon emission tomography, characterizes the physical attributes of SPECT, describes some solutions to the inherent problems encountered, and also reviews a few selected approaches in designing SPECT systems to provide high quality, artifact-free reconstructed images. It is anticipated that future developments will allow SPECT systems to more nearly attain the ultimate goal of determining absolute regional radionuclide concentration as a function of time. These systems, coupled with newly developed physiological radiopharmaceuticals, can provide useful research and clinical information.