  Understanding possible mechanisms, which can lead to suppression of helical
edge transport in Quantum Spin Hall (QSH) systems, attracted huge attention
right after the first experiments revealing the fragility of the ballistic
conductance. Despite the very intensive research and the abundance of
theoretical models, the fully consistent explanation of the experimental
results is still lacking. We systematize various theories of helical transport
with the help of the spin conservation analysis which allows one to single out
setups with the ballistic conductance being robustly protected regardless of
the electron backscattering. First, we briefly review different theories of
edge transport in the QSH samples with and without the spin axial symmetry of
the electrons including those theoretical predictions which are not consistent
with the spin conservation analysis and, thus, call for a deeper study. Next,
we illustrate the general approach by a detailed study of representative
examples. One of them addresses the helical edge coupled to an array of
Heisenberg-interacting magnetic impurities (MIs) and demonstrates that the
conductance remains ballistic even if the time-reversal symmetry on the edge is
(locally) broken but the total spin is conserved. Another example focuses on
the effects of the space-fluctuating spin-orbit interaction on the QSH edge. It
reveals weakness of the protection in several cases, including, e.g., the
presence of either the U(1)-symmetric, though not fully isotropic, MIs or
generic electron-electron interactions.
