The torsion pendulum is not only a mainstay instrument in the world of precision measurement and gravitational physics, but is important in electrical science, biophysics, petrology, metallurgy, and various other fields of endeavor. Whether used in the ``static'' (deflection) mode, the ``dynamic'' (oscillating) mode, or in some more complex configuration, instrumentation of this kind enables one to isolate and measure weak effects that would otherwise be difficult if not impossible to observe against the background gravitational field of the earth. In this review, we present a brief history of fiber-suspended apparatus and assess the fundamental limits of performance of the dumbbell pendulum. We then inventory the different versions of such systems presently used by gravitational physicists and discuss the various interrogation techniques used to monitor the movement of the suspended test mass. Next, we tabulate some of the applications for torsion instruments outside of gravitational physics, and close with a few comments on the direction of research in this area.