The statistical mechanics of local and global order in a condensed system is studied in a coarsened model in which the atomic arrangements in small volumes may be crystalline or amorphous. The melting behavior of the material is determined by two characteristic energies, the energy of an orientationally disordered locally crystalline state and the energy of a completely amorphous state. If the amorphization energy is high, the material retains local crystallinity even in the melt; then, at higher temperatures there is a crossover to a locally amorphous state. A material with a low-energy noncrystalline local packing exhibits amorphization melting; the phase transition is from an orientationally ordered crystal state to a fully amorphous melt. Strong interactions that are not of a two-body type are suggested to favor the first behavior, and to lead to structural liquids just above the melting point.