Planetary convection provides many challenges, regarding the equation of state (EoS), the coefficients of transport of momentum, heat and different species, and the governing equations. The non-linear transport of momentum causes turbulence (in the restricted sense) but the non-linear transport of heat and mass causes also a range of temporal and spatial scales, chaotic mixing, enhanced transport. Compressibility (cf. EoS), planetary rotation, dynamo action are all circumstances affecting planetary convection. In addition, the interaction between planetary envelopes, at the ICB or CMB for instance, have been shown to affect convection on one or both sides of the boundaries, with or without melting and crystallization. Mathematical, numerical and experimental studies are welcome within this broad subject.