Stirred media mills are used by the mining industry for ultrafine grinding to enhance liberation, and to decrease particle sizes of industrial minerals to tailor functional properties. This review describes stirred media mill technologies and operating principles, and summarises stress intensity theory which can be used for selecting efficient operating conditions. For fine and ultrafine grinding, the Bond work index is an inappropriate measure of grindability, so alternatives are discussed. Using literature data, the variation in the appropriate energy-size models between examples is assessed, and rationalised with stress intensity theory. A Rittinger operating index was found to be the best choice for assessing operation efficiency. Finally, a modification of stress intensity theory that tunes operating conditions based upon material properties, and the f(mat) mastercurve theory are discussed, with the conclusions that, although promising, laboratory-scale milling tests remain the most practical method of assessing material grindability and predicting industrial energy requirements. (C) 2020 Elsevier B.V. All rights reserved.