This paper has been prepared by the authors as the International Astronomical Union’s (IAU) contribution to the Task Group on Digital Representation of Units of Measure (DRUM) of the Committee on Data (CODATA) of the International Science Council (ISC). It describes the standards for use of units in astronomy and astrophysics and their development over the last 3+ decades: the IAU Style Manual, the FITS standard, and the IVOA recommendation on the use of units. In addition, it highlights special units in use in the field (units of length, time, and flux density, as well as celestial coordinates); caveats (on the importance of reference positions, linear velocities versus Doppler velocities, time, and polarization); and special quirks.

{"references": ["G.A. Wilkins, IAU Style Manual, Comm. 5, in IAU Transactions XXB (1989)", "FITS Working Group IAU Comm. 5, The FITS Standard (2018)", "S. Derriere. N. Gray, et al., IVOA Recommendation: Units in the VO (2014)", "A.H. Rots, et al., Representations of Time Coordinates in FITS, Astron. & Astroph. 574, 36 (2015)"]}