Many of the physical systems in the universe are fluids. Our understanding of the Earth, the planets, stars and even galaxies depends crucially on fluid dynamics. This mathematical discipline has been instrumental in the development of meteorology, oceanography and, to a lesser extent, astrophysics. From the beginning, observations and calculations have made apparent the rich dynamical structure of astronomical fluids: Satellite observations told us that the Great Red Spot of Jupiter was simply the most prominent object within the turbulent Jovian atmosphere, which exhibits hundreds of observable vortices embedded in a complex structure of bands or jets extending from one pole to the other. Similar structures have been observed, though in less detail, on the other Jovian planets. Complex dynamical structures are also believed to characterize condensing nebulae, evolving galaxies, stellar convective layers and the accretion disks of neutron stars and black holes.