  In this chapter we review our work on the theory of quantum transport in
topological insulator nanowires. We discuss both normal state properties and
superconducting proximity effects, including the effects of magnetic fields and
disorder. Throughout we assume that the bulk is insulating and inert, and work
with a surface-only theory. The essential transport properties are understood
in terms of three special modes: in the normal state, half a flux quantum along
the length of the wire induces a perfectly transmitted mode protected by an
effective time reversal symmetry; a transverse magnetic field induces chiral
modes at the sides of the wire, with different chiralities residing on
different sides protecting them from backscattering; and, finally, Majorana
zero modes are obtained at the ends of a wire in a proximity to a
superconductor, when combined with a flux along the wire. Some parts of our
discussion have a small overlap with the discussion in the review [Bardarson
and Moore, Rep. Prog. Phys., 76, 056501, (2013)]. We do not aim to give a
complete review of the published literature, instead the focus is mainly on our
own and directly related work.
