Very Long Baseline Interferometry (VLBI) affords astronomers their highest-resolution look at the universe. By combining the outputs of two radio astronomy antennas thousands of kilometers apart to form a Michelson interferometer, angular resolution of 1/1000 of an arcsecond or better is obtained. Current VLBI observations are limited in resolution by the largest antenna-antenna separation available (one Earth diameter), and in their information content by small number of antennas in use at one time. Extension of VLBI technique to include one or more antennas in space will relieve both of these constraints, and result in marked improvement in our ability to map distant radio sources at the highest resolution. The longer baselines which result between the space antenna and the ground antennas will substantially improve the angular resolution. The rapid movement of the space antenna around the Earth yields a wide-ranging and rapidly-changing space antenna-ground antenna separation, resulting in a much more complete map of each source. Four possible ways to extend VLBI into space include: (1) a Shuttle-attached mission, perhaps associated with the NASA advanced-technology program in large space antennas; (ii) a near-Earth orbit mission of six months to one year duration, based on a space platform associated with a Space Station; (iii) a larger-orbit free-flyer (semi-major axis about 15,000 km), of two or more years duration, such as the QUASAT satellite now being considered by NASA and ESA; and (iv) lunar and/or deep-space orbits, to reach the limits of resolution set by interstellar scattering.