  The surface of a 3D topological insulator is conducting and the topologically
nontrivial nature of the surface states is observed in experiments. It is the
aim of this paper to review and analyze experimental observations with respect
to the magnetotransport in Bi-based 3D topological insulators, as well as the
superconducting transport properties of hybrid structures consisting of
superconductors and these topological insulators. The helical spin-momentum
coupling of the surface state electrons becomes visible in quantum corrections
to the conductivity and magnetoresistance oscillations. An analysis will be
provided of the reported magnetoresistance, also in the presence of bulk
conductivity shunts. Special attention is given to the large and linear
magnetoresistance. Superconductivity can be induced in topological
superconductors by means of the proximity effect. The induced supercurrents,
Josephson effects and current-phase relations will be reviewed. These materials
hold great potential in the field of spintronics and the route towards Majorana
devices.
