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Numerical models of differentiation of a global-scale lunar magma ocean (LMO) have raised as many questions as they have answered. Recent orbital missions and sample studies have provided new context for a large range of lithologies, from the comparatively magnesian \"purest anorthosite\" reported by to Si-rich domes and spinel-rich clasts with widespread areal distributions. In addition, the GRAIL mission provided strong constraints on lunar crustal density and average thickness. Can this increasingly complex geology be accounted for via the formation and evolution of the LMO? We have in recent years been conducting extensive sets of petrologic experiments designed to fully simulate LMO crystallization, which had not been attempted previously. Here we review the key results from these experiments, which show that LMO differentiation is more complex than initial models suggested. Several important features expected from LMO crystallization models have yet to be reproduced experimentally; combined modelling and experimental work by our group is ongoing.