Free-electron lasers based on radio-frequency linear accelerators provide an important source of far-infrared radiation which allow exciting experiments that cannot be performed in any other way. Facilities such as FELIX (Nieuwegein, The Netherlands), JFEL (Newport News VA, USA), FELBE (Dresden, Germany), CLIO (Paris, France) and others provide mid- and far-infrared output in picosecond pulses with micro-joules of energy. They give continuous, wide tuning in far-IR for resonant pumping of discrete transitions (with simultaneous coverage of mid-IR) from around 3 to 250 m wavelength. This enables time-resolved spectroscopy, non-linear optics and spectroscopy of weak absorptions. They have been applied to a wide variety of problems in condensed matter physics, physical chemistry and biophysics. We review the physics applications of these sources.