Very-long-baseline interferometry (VLBI) at radio wavelengths in the
electromagnetic spectrum provides astronomers with angular resolutions as fine as 50 micro-seconds of arc. This is the highest resolution in all of astronomy and is used to focus on small scale physical processes occurring in distant cosmic sources of radiation - in ordinary stars like our Sun, star-forming regions, supernova remnants, and the most distant galaxies and quasars in our Universe. This high angular resolution is achieved by coupling individual radio telescopes together to create in effect a single instrument thousands of kilometers across. I will describe the VLBI technique, current scientific highlights in astronomy and applications in geodesy, and plans for future developments.