Topological insulators demonstrate tremendous potential in fields of electronics and magnetism for their unique boundary states that are topologically protected against backscattering at non-magnetic impurities and defects. Intriguingly, most topological insulators are also excellent thermoelectric materials, since topological insulator and thermoelectric compounds share similar material features, such as heavy elements and narrow band gaps. While the influence of topological insulator boundary states has long been neglected in early thermoelectric research, recently this neglected issue has attracted intensive research efforts. A lot of theoretical and experimental investigations have emerged to explore the contribution of topological insulator boundary states to thermoelectricity. Here, we will review the most updated theoretical and experimental progresses, trying to offer a comprehensive understanding on the relation between thermoelectric properties and topological nature. Special emphasis will be laid on the potential of topological states for improving thermoelectric properties, to pave a new way of realizing high-performance thermoelectric devices.