There is a storied scientific history in the role of mechanical instruments for the measurement of fundamental physical interactions. Among these include the detection of magnetic torques via a displacement of a compliant mechanical sensor as a result of angular momentum transfer. Modern nanofabrication methods have enabled the coupling of mechanical structures to single, miniature magnetic specimens. This has allowed for strikingly sensitive detection of magnetic hysteresis and other quasi-static effects, as well as spin resonances, in materials confined to nanoscale geometries. The extraordinary sensitivities achieved in mechanical transduction through recent breakthroughs in cavity optomechanics, where a high-finesse optical cavity is used for readout of motion, are now being harnessed for torque magnetometry. In this article, we review the recent progress in mechanical detection of magnetic torques, highlight current applications, and speculate on possible future developments in the technology and science. Guidelines for designing and implementing the measurements are also included.