Despite the advantages of semiconductor field-effect transistors (FETs), they have yet to show competing responses in terahertz (THz) radiation detection compared to other techniques. It is therefore important to improve our understanding of the FET operation when detecting THz radiation beyond its cut-off frequency. The journey of modeling THz detection in FET started with the plasma wave model by Dyaknov and Shur and proceeded to other approaches to develop a physics-based model of the FET nonlinearity that drives the high-frequency rectification. This work presented a review of the models developed to model the operation of FEET detectors. The common factors as well as the advantages of each model are emphasized. The more we understand these models, the better we can guide the development of FET designs for higher detection responses.