  One of the actual challenges of spintronics is the realization of a
spin-transistor allowing to control spin transport through an electrostatic
gate. In this review, we report on different experiments which demonstrate a
gate control of spin transport in a carbon nanotube connected to ferromagnetic
leads. We also discuss some theoretical approaches which can be used to analyze
spin transport in these systems. We emphasize the roles of the gate-tunable
quasi-bound states inside the nanotube and the coherent spin-dependent
scattering at the interfaces between the nanotube and its ferromagnetic
contacts.
