Thermoelectric devices are used for the conversion of thermal and electrical energy. They offer a number of advantages over competing technologies including scalability to small sizes and temperature differences, simple reliable designs and often low cost. However, these devices have not seen wide application in energy applications due to their limited conversion efficiency. This is a consequence of the limited performance of current thermoelectric materials, which can be characterized by a dimensionless figure of merit, ZT=σS2T/κ. There is no known fundamental limit on ZT. However, the combination of transport parameters entering ZT is a combination that does not occur in ordinary materials. This talk presents an overview of ZT and discusses strategies for optimizing ZT as well as recent results that point to ways of identifying new high ZT compositions. An important finding is that electronic structure plays a remarkably subtle role in thermoelectric performance that can however be simply visualized in terms of iso-energy surfaces. Finally, a connection is drawn between topological insulators and high ZT thermoelectrics, explaining the overlap between these two interesting materials classes. Characteristics that can be used to identify new thermoelectric compositions are presented and discussed.