Astrometry provides the foundation for astrophysics. Accurate positions are required for the association of sources detected at different times or wavelengths, and distances are essential to estimate the size, luminosity, mass, and ages of most objects. Very long baseline interferometry at radio wavelengths, with diffraction-limited imaging at submilliarcsecond resolution, has long held the promise of microarcsecond astrometry. However, only in the past decade has this been routinely achieved. Currently, parallaxes for sources across the Milky Way are being measured with ˜10 μas accuracy, and proper motions of galaxies are being determined with accuracies of ˜1 μas year-1. The astrophysical applications of these measurements cover many fields, including star formation, evolved stars, stellar and supermassive black holes, Galactic structure, the history and fate of the Local Group, the Hubble constant, and tests of general relativity. This review summarizes the methods used and the astrophysical applications of microarcsecond radio astrometry.