Thermal convection occurs in most objects that populate our Universe, whenever radiation is insufficient to transport the heat because the medium is too opaque. In astrophysical objects convection involves a wide range of spatial and temporal scales - experts call this turbulence - which makes it rather difficult to model. For this reason convection remains one of the major uncertainties when modeling stars and planets, and this is partly true also for accretion disks. However, substantial progress has been achieved during the past years, both in the numerical simulation of convective regions and in the observation of convective flows by various new techniques.