It is natural to inquire whether thermal convection is occurring in the Moon through solid state creep processes. The primary evidence is the departure of the Moon from the figure of hydrostatic equilibrium, but certain difficulties in the thermal history of the Moon are eased by assuming heat transfer by convection. If convection exists in the Moon it must have a second harmonic pattern, otherwise the lunar moments of inertia would not differ.Two important predictions of the marginal theory of convection: the existence of a core of radius 0.06–0.3 of the lunar radius (for a second ergee harmonic) and the value of 0.4 for the ratio of the dynamical to surface ellipticities now have support, the latter from the data of the heights of the lunar surface. The former prediction is compatible with the value of the moment of inertia factor now found if the Moon's interior is ‘hot’.Further the existence of a fluid iron core 3400 m.y. ago seems required as a result of the remanent magnetization of the crystalline rocks of the maria basins inferred from the remanent magnetization of the returned Apollo samples and the fields measured by the Apollo 12 and Explorer magnetomers.