Here we critically examine the geophysical and geochemical properties of the Moon in order to identify the extent to which dynamical scenarios satisfy these observations. New joint inversions of existing lunar geophysical data (mean mass, moment of inertia, and tidal response) assuming a laterally- and vertically homogeneous lunar mantle show that, in all cases, a core with a radius of 300±20 km (∼0.8 to 1.5 % the mass of the Moon) is required. However, an Earth-like Mg# (0.89) in the lunar mantle results in core densities (7800±100 kg/m3) consistent with that of Fe-Ni alloy, whereas FeO-rich compositions (Mg# = 0.80--0.84) require lower densities (6100±800 kg/m3). Geochemically, we use new data on mare basalts to reassess the bulk composition of the Moon for 70 elements, and show that the lunar core likely formed near 5 GPa, 2100 K and ∼1 log unit below the iron-wüstite buffer. Moreover, the Moon is depleted relative to the Earth's mantle in elements with volatilities higher than that of Li, with this volatile loss likely having occurred at low temperatures (1400±100 K), consistent with mass-dependent stable isotope fractionation of moderately volatile elements (e.g., Zn, K, Rb). The identical nucleosynthetic (O, Cr, Ti) and radiogenic (W) isotope compositions of the lunar and terrestrial mantles, strongly suggest the two bodies were made from the same material, rather than from an Earth-like impactor. Rb-Sr in FANs and Lu-Hf and Pb-Pb zircon ages point Moon formation close to ∼4500 Ma. Taken together, there is no unambiguous geochemical or isotopic evidence for the role of an impactor in the formation of the Moon, implying perfect equilibration between the proto-Earth and Moon-forming material or alternative scenarios for its genesis.