Basic features of electronic transport in granular systems consisting of magnetic metallic grains distributed in a non-magnetic and non-conducting matrix will be reviewed and discussed. The discussion will be particularly focused on the mechanism of electron transport through the inter-grain barriers. When the grains are of a nanometer size, the effects due to discrete charging of the grains with single electrons become important and lead to observable effects at low temperatures. When additionally an external magnetic field is applied to the system, magnetic moments of the grains align along the field and this leads to a decrease in the resistance. Basic features of such a magnetoresistance effect will be discussed, including enhancement of the effect in the Coulomb blockade regime due to co-tunnelling processes.
An interesting limiting situation occurs when electric current flows through a single grain or through a one-dimensional array of a few grains, coupled to two ferromagnetic electrodes. Such a case may be considered as a ferromagnetic single-electron transistor, in which the discrete charging effects lead to Coulomb blockade phenomenon and Coulomb oscillations when an additional gate voltage is applied. Moreover, charging effects lead to magnetoresesistace oscillations with increasing bias voltage. An important role in electronic transport plays a nonequilibrium magnetic moment induced on the grain by flowing current (so-called spin accumulation). Spin-flip processes on the grains reduce the spin accumulation and therefore are important as well. Detailed theoretical description of such systems will be presented and the predictions will be compared with experimental results presented in recent literature.

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