It is one of the oldest subfields of the science, dating back at least to Hipparchus, who compiled the first catalogue of stars visible to him and in doing so invented the brightness scale basically still in use today. In 1750, Simon Newcomb founded modern Astrometry.
Apart from the fundamental function of providing Astronomers with a reference frame to report their observations in, Astrometry is also fundamental for fields like celestial mechanics, stellar dynamics and galactic astronomy. It is also instrumental for keeping time, in that UTC is basically the atomic time synchronized to Earth's rotation by means of exact observations.
There have been several important advances in astrometry.
Another was the use of Cepheid variable stars to measure the distance to nebulae, which led to the discovery of other galaxies by Edwin Hubble. Hubble used triangulation on nearby Cepheids, and correlated the Cepheid's period to their absolute brightness. Then by measuring the period and brightness of Cepheids in nebulae, he established their distance by their brightness.
Hubble used Cepheids to discover and calibrate distance with the red shift shown by distant galaxies.
From 1989 to 1993, the European Space Agency's Hipparcos satellite performed astrometric measurements resulting in a catalogue of positions accurate to 20-30 milliarcsec for over a million stars.