Current status of our understanding of magnetotransport in magnetic multilayers

We review the current theoretical understanding of giant magnetoresistance in magnetic multilayered structures. The active ingredients producing magnetoresistance for current in and perpendicular to the plane of the layers are discussed, and the effect of superlattice band structure on transport is reviewed. Differences between ballistic and diffusive electron transport are highlighted. The effective fields used to account for vertex corrections for current perpendicular to the layers is discussed and their meaning is defined.