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A quasi one-dimensional model of spin transport in heterogeneous media based on the Boltzmann equation is presented in order to define the basic properties characterizing perpendicular spin transport in nanostructures. Experimental results are reviewed, first on the giant magnetoresistance of magnetic multilayers: spin dependent scattering in bulk and at interfaces, spin-diffusion length in the ferromagnetic layers and in the non-magnetic spacers. The observations of magnetoresistance associated with spin-scattering at Bloch walls are summarized. The junction magnetoresistance of ferromagnetic-insulator-ferromagnetic structures are reviewed, including the tunnel junctions produced with materials which present colossal magnetoresistance. An outlook on possible devices and novel structures is given.