Available evidence strongly suggests that the HED (howardite, eucrite, diogenite) meteorites are samples of asteroid 4 Vesta. Abundances of the moderately siderophile elements (Ni, Co, Mo, W and P) in the HED mantle indicate that the parent body may have been completely molten during its early history. During cooling of a chondritic composition magma ocean, equilibrium crystallization is fostered by the suspension of crystals in a convecting magma ocean until the crystal fraction reaches a critical value near 0.80, when the convective system freezes and melts segregate from crystals by gravitational forces. The extruded liquids are similar in composition to Main Group and Stannern trend eucrites, and the last pyroxenes to precipitate out of this ocean (before convective lock-up) span the compositional range of the diogenites. Subsequent fractional crystallization of a Main Group eucrite liquid, which has been isolated as a body of magma, produces the Nuevo Laredo trend and the cumulate eucrites. The predicted cumulate mineral compositions are in close agreement with phase compositions analyzed in the cumulate eucrites. Thus, all HED meteorites are shown to have formed as part of a simple and continuous crystallization sequence starting with a magma ocean environment on an asteroidal-sized parent body, consistent with Vesta.