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Space missions have shown that most terrestrial bodies have an internally generated magnetic field in their metallic core and/or a crustal field due to remanent magnetism. The latter indicates the presence of an old dynamo at the time of crust formation. Information on the two together helps to uncover the body’s magnetic field history, and it is generally accepted that convection flows driven by thermal or compositional buoyancy in the cores are the most likely source for maintaining global planetary magnetic fields. The convection flow in the core, in turn, is closely related to the interior dynamics of the mantles above and the thermal evolution of the body. This chapter describes the mechanisms for dynamo generation either by thermal or compositional convection in the core. It discusses the magnetic field evolution of Mercury, Moon, Mars, Ganymede, and planetesimals and will also address the possibility of dynamo generation in rocky exoplanets