  Topological insulators (TIs) are materials that have a bulk electronic band
gap like an ordinary insulator but have protected conducting states on their
surface. One of the most interesting properties of TIs is their spin helicity,
whereby the spin is locked normal to the wave vector of the surface electronic
state. The topological surface states should be very stable in TIs, since these
spin-textured surface states are robust against spin-independent
backscattering. Scattering from defects and other lattice imperfections is
possible provided the spin is not completely flipped. However, the quality of
TI crystals can be controlled by careful growth, whereas phonons will exist in
even the most perfect crystals. Consequently, electron-phonon coupling (EPC)
should be the dominant scattering mechanism for surface electronic states at
finite temperatures. Hence, the study of EPC in TIs is of exceptional
importance in assessing any potential applications. In this article both
experimental and theoretical studies of the EPC on the surface of TIs are
reviewed, with the contents mainly focused on the typical strong three
dimensional TIs, such as Bi2Se3 and Bi2Te3.
