This paper provides a 40-year review of the infrared imaging system modeling activities at the U.S. Army Night Vision and Electronic Sensors Directorate (NVESD). The result of these modeling activities is a system model that describes the target ac- quisition performance of a human observer and an infrared im- ager. The model has been adopted by the military infrared imaging community as an assessment of how well an ensemble of observers perform the tasks of target detection, recognition, and identifica- tion. The model is used in infrared imager design and assessment, where military users understand how the metrics predicted by the model relates to system performance on the battlefield. This review begins with early work in the late 1950s and proceeds to present day modeling successes. Finally, the infrared imaging system mod- eling activities for the future are discussed. Index Terms—Infrared imaging, modeling.