  Topological states of matter have attracted a lot of attention due to their
many intriguing transport properties. In particular, two-dimensional
topological insulators (2D TI) possess gapless counter propagating conducting
edge channels, with opposite spin, that are topologically protected from
backscattering. Two basic features are supposed to confirm the existence of the
ballistic edge channels in the submicrometer limit: the 4-terminal conductance
is expected to be quantized at the universal value $2e^{2}/h$, and a nonlocal
signal should appear due to a net current along the sample edge, carried by the
helical states. On the other hand for longer channels the conductance has been
found to deviate from the quantized value. This article reviewer the
experimental and theoretical work related to the transport in two-dimensional
topological insulators (2D-TI), based on HgTe quantum wells in zero magnetic
field. We provide an overview of the basic mechanisms predicting a deviation
from the quantized transport due to backscattering (accompanied by spin-flips)
between the helical channels. We discuss the details of the model, which takes
into account the edge and bulk contribution to the total current and reproduces
the experimental results.
