  This paper reviews recent developments in quantum transport and it presents
recent efforts to explore the contribution of topological insulator boundary
states to thermoelectricity in Bi$_2$Te$_3$ thin films. Although Bi$_2$Te$_3$
has been used as a thermoelectric material for many years, it is only recently
that thin films of this material have been synthesized as 3D topological
insulators with interesting physics and potential applications related to
topologically protected surface states. A major bottleneck in Bi$_2$Te$_3$ thin
films has been eliminating its bulk conductivity while increasing its crystal
quality. The ability to grow epitaxial films with high crystal quality and to
fabricate sophisticated Bi$_2$Te$_3$-based devices is attractive for
implementing a variety of topological quantum devices and exploring the
potential of topological states to improve thermoelectric properties. Special
emphasis is laid on preparing low-defect-density Bi$_2$Te$_3$ epitaxial films,
gate-tuning of normal-state transport and Josephson supercurrent in topological
insulator/superconductor hybrid devices. Prospective quantum transport
experiments on Bi$_2$Te$_3$ thin-film devices are discussed as well. Finally,
an overview of current progress on the contribution of topological insulator
boundary states to thermoelectricity is presented. Future explorations to
reveal the potential of topological states for improving thermoelectric
properties of Bi$_2$Te$_3$ films and realizing high-performance thermoelectric
devices are discussed.
