Despite the availability of an advanced system of geostationary satellites covering the United States, the detection of severe or violent thunderstorms has been dependent mainly on radar and storm spotters, when available. In Europe and Africa, radar and spotter networks are less developed or nonexistent. The question arises, to what extent can satellites be used for detecting severe weather phenomena? Research into this question started with the first satellite observations more than 40 years ago in the United States. This paper reviews the principal findings from this research, with some current applications of the satellite data. The emphasis will be on inferring the intensity or severity of existing thunderstorms, which includes the occurrence of damaging winds, hail, and tornadoes. The estimation of rainfall from satellite imagery and the use of the data in numerical weather prediction are important topics, but beyond the scope of this paper. However, storm initiation and intensification will be covered briefly.