Very-long-baseline interferometry (VLBI) is a novel observing technique for measuring the relative positions of widely separated points on the surface of the Earth with centimeter-level accuracy. Such accuracy is two or three orders of magnitude better than was available with classical techniques only a few decades ago. This enormous improvement in accuracy has opened up for study a broad new spectrum of geophysical phenomena. The new measurements allow direct observation of the tectonic motions and deformations of the Earth's crustal plates, observations of unprecedented detail of the variations in the rotation of the Earth, and direct measurement of the elastic deformations of the Earth in response to tidal forces. These new measurements have placed significant constraints on models of the interior structure of the Earth; for example, measurements of the variations in the Earth's nutation have been shown to be particulary sensitive to the shape of the core-mantle boundary. The VLBI measurements, coupled with other space-based geodetic observing techniques such as the Global Positioning System, allow construction of a global reference frame accurate at the centimeter level. Such a frame will be essential to studying long-term global changes, especially those changes related to sea-level variations as recorded by tide gauge measurements.