Interferometry with the NAVSTAR Global Positioning System (GPS) is the most efficient method of establishing three-dimensional geodetic control on local and regional scales. This is already true, even though the constellation of satellites is incomplete. We consider some theoretical and practical aspects of using differenced carrier-phase observations of the GPS satellites to establish three-dimensional control networks. We present simple and efficient algorithms for processing multi-station, multi-satellite observations. These algorithms have been used to establish three-dimensional control networks. Under widely varying conditions, we have obtained accuracies of 1 to 1.5 parts per million (ppm) in all three coordinates, or by 1 to 3 cm for the coordinates differences between network stations separated 10 to 20 km. when interferometry is used also to determine the satellite orbits, we anticipate improvement of the accuracy of regional control networks to the level of 0.1 ppm. Keywords: Geodesy; Geodetic control; Geodetic networks; Three dimensional geodesy; Satellite geodesy; NAVSTAR Global Positioning System; and Interferometry.