Iron meteorites are macroscopic single-crystals of Ni-Fe alloy (ave, 10% Ni), segregated into strongly ferro-magnetic (α) and weakly magnetic (γ) phases, intergrown in the octahedral system. Given their probable origin as molten metal cores or pods, slowly cooled (at rates -1-100°C/my) in asteroidal bodies, they seem ideally suited to record ancient magnetic fields as thermal (TRM) or thermochemical (TCRM) remanent magnetization. To test this hypothesis, we investigated the intensity, relative stability and directional behavior in AF demagnetization of the natural (NRM), saturation (IRM_s), thermal (TRM) and spontaneous (SM) magnetization in several iron meteorites spanning the compositional-structural spectrum. The main results are: 1) The remanence intensity and relative stability increase systematically from the coarser to the finer-grained classes. The latter are capable of carrying a stable paleoremanence. 2) The NRM coercivity spectra, which are considerably harder than laboratory TRM's in the finest structured groups, gradually soften as grain-size coarsens. 3) All magnetization directions (NRM, TRM, SM) in octahedrites appear to be preferentially associated with the octahedral γ{111} crystallographic planes on which α{110} plates nucleated and grew, and/or aligned with their intersections. The finer the structure, the clearer the link of magnetization directions to ‘easy’ crystallographic planes and axes. 4) A direct comparison of NRM and TRM demagnetization curves yields paleointensities in the range 0.3-3 Oe. However, the similarity of SM's (following zero-field cooling) to TRM's, implies fictitious ambient field values of 2-5 Oe. The extent to which SM mimics the TRM and NRM characteristics severely limits attempts to establish that the stable NRM in iron meteorites is an ancient TRM acquired in extraterrestrial fields of -1 Oe. It is evident that the combined effect of magnetocrystalline and shape-anisotropy of the crystallographically ordered ferromagnetic kamacite (α)-phase had an overriding importance in producing the observed magnetic remanence characteristics of iron meteorites. Therefore, no reliable information regarding the presence, strength and sources of ancient solar-system fields can be retrieved from iron meteorites.