Owing to its high brilliance, infrared and terahertz synchrotron radiation (IR/THz-SR) has emerged as a powerful tool for spectroscopy under extreme (i.e., technically more difficult) experimental conditions such as high pressure, high magnetic field, high spatial resolution, and a combination of these. The methodologies for pressure-and magneticfield-dependent spectroscopy and microscopy using IR/THz-SR have advanced rapidly worldwide. By applying them to strongly correlated electron systems (SCESs), many experimental studies have been performed on their electronic structures and phonon/molecular vibration modes under extreme conditions. Here, we review the recent progress of methodologies of IR/THz-SR spectroscopy and microscopy, and the experimental results on SCESs and other systems obtained under extreme conditions.