We analyze the interplay between disorder and band structure in current perpendicular to the planes giant magnetoresistance (GMR). We consider finite magnetic multilayers attached to pure crystalline leads, described by a tight-binding simple cubic two-band model (s-d). Several models of disorder are considered, including random on-site potentials, lattice distortions, impurities, vacancies, and cross-section fluctuations. Magnetotransport properties are calculated in the zero-temperature zero-bias limit, within the Landauer-Buttiker formalism. Using a very efficient numerical scattering technique, we are able to perform simulations, over large length scales, and to investigate spin transport in the ballistic, diffusive, and localized regimes, as well as the crossover between them. The competition between disorder-induced mean-free-path reduction and disorder-induced spin asymmetry enhancement of the conductance highlights several different regimes of GMR. [S0163-1829(99)01534-9].