Thermoelectric devices have gained importance in recent years as viable solutions for applications such as spot cooling of electronic components, remote power generation in space stations and satellites etc. These solid-state devices have long been known for their reliability rather than their efficiency; they contain no moving parts, and their performance relies primarily on material selection, which has not generated many excellent candidates. Research in recent years has been focused on developing both thermoelectric structures and materials that have high efficiency. In general, thermoelectric research is two-pronged with (1) experiments focused on finding new materials and structures with enhanced thermoelectric performance and (2) analytical models that predict thermoelectric behavior to enable better design and optimization of materials and structures. While numerous reviews have discussed the importance of and dependence on materials for thermoelectric performance, an overview of how to predict the performance of various materials and structures based on fundamental quantities is lacking. In this paper we present a review of the theoretical models that were developed since thermoelectricity was first observed in 1821 by Seebeck and how these models have guided experimental material search for improved thermoelectric devices. A new quantum model is also presented, which provides opportunities for the optimization of nanoscale materials to enhance thermoelectric performance.