The asteroid 4 Vesta is one of the very few heavenly bodies to have been linked to samples on Earth: the howardite-eucrite-diogenite (HED) meteorite suite. This large and diverse suite of meteorites provides a detailed picture of Vesta's igneous and postigneous history. We have used the range of igneous rock types and compositions in the HED suite to test a series of chemical models for solidification processes following peak melting (magma ocean) conditions on Vesta. Fractional crystallization cannot have been a dominant early process in the magma ocean because it leads to excessive Fe-enrichment in the melt. Models that are dominated by equilibrium crystallization cannot produce orthopyroxene cumulates (diogenites). Our best models invoke 60–70% equilibrium crystallization of a magma ocean followed by continuous extraction of the residual melt into shallow magma chambers. Fractional crystallization in these magma chambers combined with continuous or periodic addition of more melt from the slowly compacting crystal mush (magmatic recharge) can produce all of the igneous HED lithologies (noncumulate and cumulate eucrites, diogenites, dunites, harzburgites, and olivine diogenites). Magmatic recharge can also explain the narrow range in eucrite compositions and the variability of incompatible trace element concentrations in diogenites. We predict an internal structure for Vesta that permits excavation of the HEDs during the formation of the Rheasilvia basin, while remaining consistent with observations from the Dawn mission and most impact models.