Mixing in the radiative zones of stars is one of the least well understoodcomponents of stellar evolution, and yet can, in many instances, play acrucial role. In recent years, however, much progress has been made inquantifying mixing by a variety of hydrodynamic instabilities, thanks tonumerical experiments that have strongly benefited from advances insupercomputing. I will review the state of the field, and presentperspectives on what can and should be done next by the stellar evolutioncommunity, and by the astrophysical fluid dynamics community.
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