Various types of mechanisms for giant magnetoresistance, in particular forf‐electron systems, are critically reviewed. First, the most typical prototype of the nesting‐type magnetic ordering in the heavy‐rare‐earth metals is reviewed. Both negative and positive magnetoresistances are expected for the resistivities, parallel and perpendicular to the nesting wave vector, respectively. Then, the most typical negative magnetoresistance due to impurity states is studied on Eu chalcogenides with chalcogen vacancies or with trivalent rare‐earth impurities substituting Eu atoms. In the former, the change from the singlet to the triplet for the trapped pair electrons is the main origin. In both cases magnetic polarons play important roles. For low‐carrier‐density systems in the metallic region ferromagnetic ordering is induced; the resistivity then has a peak at a temperature near aboveTcdue to a critical scattering resulting a negative magnetoresistance. Narrow‐gap semiconductors and low‐carrier semimetals are also typical materials to show exotic giant magnetoresistance. Various other cases including valence fluctuating systems are also studied. ©1995 American Institute of Physics.