There is a conspicuous dichotomy in the conventional model of lunar petrogenesis between the total intra-crustal differentiation postulated for the products of feldspathic volcanism in the lunar highlands and the near absence of differentiation postulated for the products of mare volcanism. Both the cumulate mantle model, and the selenotherm postulated to accompany genesis of alleged ‘primary’ mare magmas by remelting of those cumulates, imply supra-adiabatic thermal gradients in near-solidus materials throughout the lunar mantle 4·3–3·2 Ga ago. This should have resulted in vigorous convective motion, which has not occurred. There is no positive europium anomaly in the average lunar highland crust. That crust cannot, therefore, have formed by plagioclase flotation from a lunar magma ocean, for which there is no other requirement. There is no negative europium anomaly in the average mantle to be inherited by later mare basalts. Other rocky bodies of lunar size in the Solar System have accreted at rates that allowed incorporation of plenty of volatiles and without forming global magma oceans. Partial melting in the presence of water, followed by near-surface fractionation and volatile losses can explain the feldspathic character, high incompatible element concentrations and lack of Eu anomaly in the lunar highlands. Volcanic eruption on the Moon must have been accompanied by selective volatilization losses of sodium, sulphur and other elements similar to the process seen on Io, which can account for the major differences between terrestrial and lunar basalts. Siderophile element depletion in lunar lavas may reflect immiscible sulphide liquid and metal separation, rather than global impoverishment in such elements, and large ore bodies may have formed close to the lunar surface. Mare basalt volcanism appears to have been a protracted, low magma productivity event with few similarities to terrestrial ocean-floor, ocean-island, continental flood basalt or komatiite volcanism. At low pressure the crystallization of plagioclase well before pyroxene typifies those terrestrial mid-ocean ridge basalt, ocean-island basalt and continental flood basalt magmas. A similar sequence is demanded of the postulated lunar primary magmas. Mare basalt hand-specimen and pyroclastic glass bead compositions do not, however, display the required crystallization sequence and cannot represent the required primary melt compositions. The true erupted lava compositions which gave rise to the regolith compositions across all the maria are much more feldspathic than the majority of large hand specimens and, in common with basalts on other planets, they are close to low-pressure plagioclase-saturated cotectic residual liquids which have evolved by removal of gabbros in crustal magma chambers, or perhaps in giant lava lakes akin to topless Bushveld complexes. Any further debate could be resolved by a 100 m drill core in a few mare locations. Field provenance of samples from Mars, a planet half covered by flood basalts and products of central volcanoes, will be little better than for those from the Moon. It will be important to encourage multiple working hypotheses, rather than to rush to a consensus.