To better understand the geology of metallic asteroids and the crystallization of planetary cores, we have studied the crystallization of the cores of iron meteorite parent bodies. Available data for the relative magnitudes of the adiabatic gradient and the liquidas gradient across the core indicate that for the low pressures of asteroidal cores (less than a few hundred megapascals), crystallization commences at the base of the mantle and continues as dominantly inward growth. A consequence of the rejection of S from the crystallizing solid is that a light S-rich layer forms below the crystallizing front. This inhibits concentric front growth and promotes formation of tree-like crystals called dendrites. The mode of crystallization was therefore completely different from that of Earth. Dendrites in asteroidal cores may have grown to lengths of hundreds of meters or perhaps even as large as the core radius thereby dividing the core into separate magma chambers. Supporting evidence comes from the Cape York iron meteorites and others from the same core: the surface area of the solid/liquid interface was very large; the direction of crystallization was horizontal; and the liquid was not perfectly mixed throughout crystallization. We argue that the Cape York irons did not form as a result of a rare event; they are typical products of core crystallization. Troilite, which has different optical and mechanical properties from Fe-Ni, formed in pockets between dendrites. The distribution of troilite may therefore provide a visual record of the crystallization history of asteroidal cores.