  Topology in condensed matter physics manifests itself in the emergence of
edge or surface states protected by underlying symmetries. We review
two-dimensional topological insulators whose one-dimensional edge states are
characterized by spin-momentum locking and protected by time-reversal symmetry.
We focus in particular on their transport properties in the presence of
electron interactions, which can allow the onset of different backscattering
mechanisms, thus leading to deviations from the quantized conductance observed
in the ballistic regime. The combined presence of helicity and electron
interactions creates a new paradigm of the one-dimensional world called helical
Luttinger liquid, whose theoretical properties and experimental observations
are reviewed.
