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Among the great diversity of atmospheric circulation patterns observed throughout the solar system, polar vortices stand out as a nearly ubiquitous planetary‐scale phenomenon. In recent years, there have been significant advances in the observation of planetary polar vortices, culminating in the fascinating discovery of Jupiter's polar vortex clusters during the Juno mission. Alongside these observational advances has been a major effort to understand polar vortex dynamics using theory, idealized and comprehensive numerical models, and laboratory experiments. Here, we review our current knowledge of planetary polar vortices, highlighting both the diversity of their structures, as well as fundamental dynamical similarities. We propose a new convention of vortex classification, which adequately captures all those observed in our solar system, and demonstrates the key role of polar vortices in the global circulation, transport, and climate of all planets. We discuss where knowledge gaps remain, and the observational, experimental, and theoretical advances needed to address them. In particular, as the diversity of both solar system and exoplanetary data increases exponentially, there is now a unique opportunity to unify our understanding of polar vortices under a single dynamical framework. Plain Language Summary: Polar vortices are often described as the rotational motion of air in the polar regions of planets, this includes large vortices where flow circumnavigates the pole and smaller vortices that are centered within polar regions. The most commonly discussed polar vortices are those in Earth's stratosphere, which have given rise to the ozone hole. More recently a number of other circulation patterns have been described as polar vortices, on Earth, and other planets. We review key features of these different polar vortices, and explain their similarities and differences using decades of theory, observations and modeling from the geophysical fluid dynamics community. We review how the different dynamical and chemical structures evolve as features of the polar vortex structures, and why they are integral to the makeup of planetary atmospheres. We conclude by summarizing the latest knowledge on potential polar vortices outside of our solar system, which to date are only theorized. Key Points: Earth is not unique in having polar vortices, every well‐observed planetary body with a substantial atmosphere appears to have oneThe range of vortices in our solar system is diverse, but much of their character can be explained in terms of the fluid dynamics for EarthClassifying vortices into those with predominantly circumpolar flow and those with large zonal asymmetries captures all that we know about [ABSTRACT FROM AUTHOR]