Polar vortices that share many similarities are found in Earth's stratosphere and the atmospheres of Mars and Saturn's moon Titan. These vortices all occur in the winter, and are characterized by high potential vorticity (PV) in polar regions, steep meridional PV gradients and peak zonal winds in middle latitudes, and a cold pole. There are, however, differences in the daily and subseasonal variability, zonal asymmetries, and PV structure among the vortices. These differences are related to differences in the disruption of polar vortices by Rossby waves, the poleward extent of the mean meridional circulation, and condensation of major gases. There are also differences in the transport of gases and particles among the vortices. The range of polar vortex characteristics is likely much larger for terrestrial exoplanets, which include planets with, for example, a wider range of obliquities. Expected final online publication date for the Annual Review of Fluid Mechanics, Volume 55 is January 2023. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.