Fourier transform spectrometers (FTS), mostly working in infrared (IR) or near infrared (NIR) range, provide a variety of chemical or material analysis with high sensitivity and accuracy and are widely used in public safety, environmental monitoring and national border security, such as explosive detection. However, because of being bulky and expensive, they are usually used in test centers and research laboratories. Miniaturized FTS have been developed rapidly in recent years, due to the increasing demands. Using micro-electromechanical system (MEMS) micromirrors to replace the movable mirror in a conventional FTS system becomes a new realm. This paper first introduces the principles and common applications of conventional FTS, and then reviews various MEMS based FTS devices.