The sensitivity of microelectromechanical system (MEMS) devices to radiation is reviewed, with an emphasis on radiation levels representative of space missions rather than of operation in nuclear reactors. As a purely structural material, silicon has shown no mechanical degradation after radiation doses in excess of 100 Mrad. MEMS devices, even when excluding control/readout electronics, have, however, failed at doses of only 20 krad, though some devices have been shown to operate correctly for doses greater than 10 Mrad. Radiation sensitivity depends strongly on the sensing or actuation principle, device design, and materials, and is linked primarily to the impact on device operation of radiation-induced trapped charge in dielectrics. MEMS devices operating on electrostatic principles can be highly sensitive to charge accumulation in dielectric layers, especially for designs with dielectrics located between moving parts. In contrast, thermally and electromagnetically actuated MEMS are much more radiation tolerant. MEMS operating on piezoresitive principles start to slowly degrade at low doses, but do not fail catastrophically until doses of several Mrad. A survey of all published reports of radiation effects on MEMS is presented, as well as a summary of techniques that can improve their radiation tolerance.