Spin-dependent coherent quantum transport through carbon nanotubes (CNT) is studied theoretically within a tight-binding model and the Greens function partitioning technique. End-contacted metal/nanotube/metal systems are modelled and next studied in the magnetic context, i.e. either with ferromagnetic electrodes or at external magnetic fields. The former case shows that quite a substantial giant magnetoresistance (GMR) effect occurs ($pm 20%$) for disorder-free CNTs. Anderson-disorder averaged GMR, in turn, is positive and reduced down to several percent in the vicinity of the charge neutrality point. At parallel magnetic fields, characteristic Aharonov-Bohm-type oscillations are revealed with pronounced features due to a combined effect of: length-to-perimeter ratio, unintentional electrode-induced doping, Zeeman splitting, and energy-level broadening. In particular, a CNT is predicted to lose its ability to serve as a magneto-electrical switch when its length and perimeter become comparable. In case of perpendicular geometry, there are conductance oscillations approaching asymptotically the upper theoretical limit to the conductance, $4 e^2/h$. Moreover in the ballistic transport regime, initially the conductance increases only slightly with the magnetic field or remains nearly constant because spin up- and spin down-contributions to the total magnetoresistance partially compensate each other.
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