  An important consequence of the discovery of giant magnetoresistance in
metallic magnetic multilayers is a broad interest in spin dependent effects in
electronic transport through magnetic nanostructures. An example of such
systems are tunnel junctions -- single-barrier planar junctions or more complex
ones. In this review we present and discuss recent theoretical results on
electron and spin transport through ferromagnetic mesoscopic junctions
including two or more barriers. Such systems are also called ferromagnetic
single-electron transistors. We start from the situation when the central part
of a device has the form of a magnetic (or nonmagnetic) metallic nanoparticle.
Transport characteristics reveal then single-electron charging effects,
including the Coulomb staircase, Coulomb blockade, and Coulomb oscillations.
Single-electron ferromagnetic transistors based on semiconductor quantum dots
and large molecules (especially carbon nanotubes) are also considered. The main
emphasis is placed on the spin effects due to spin-dependent tunnelling through
the barriers, which gives rise to spin accumulation and tunnel
magnetoresistance. Spin effects also occur in the current-voltage
characteristics, (differential) conductance, shot noise, and others. Transport
characteristics in the two limiting situations of weak and strong coupling are
of particular interest. In the former case we distinguish between the
sequential tunnelling and cotunneling regimes. In the strong coupling regime we
concentrate on the Kondo phenomenon, which in the case of transport through
quantum dots or molecules leads to an enhanced conductance and to a pronounced
zero-bias Kondo peak in the differential conductance.
