  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 sub-milliarcsec resolution,
has long held the promise of micro-arcsecond 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 uas accuracy and proper
motions of galaxies are being determined with accuracies of ~1 uas/y. The
astrophysical applications of these measurements cover many fields, including
star formation, evolved stars, stellar and super-massive 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 micro-arcsecond radio astrometry.
