The aim of this colloquium is to provide an overview of our current knowledge of the structure, composition and dynamics of the mantles and cores of planets and rocky moons, including those of "super-Earths", modeled from remote sensing observations from Earth, and from past and recent planetary missions. The colloquium will include presentations by leading specialists from different disciplines, as well as a debate with the aim of identifying promising directions in the near future for both the acquisition of new observations and modeling.