Energy converters based on the thermoelectric effect are solid-state devices with no moving parts and they are extremely reliable and scalable. They can be optimised for power generation or for cooling. Traditional thermoelectric modules are formed with legs with positive and negative charge carriers connected electrically in series and thermally in parallel. The design of a thermoelectric module involves multiple issues related to integration, quality of the contacts, mechanical and thermal stability and cost and environmental compatibility. These aspects are certainly important for the development of the technology, but the practical value depends critically on the availability of materials that can provide efficient thermoelectric conversion. The principles and methods of solid-state physics and physical chemistry govern the microscopic properties of the materials used for the legs, and the development of thermoelectricity has been guided by an interesting synergy between experiments and theoretical efforts at the level of phenomenological models, and also from first-principles quantum mechanical calculations. Simple models help to rationalise trends and the results of measurements; quantum mechanical calculations contribute fully controlled ‘simulated experiments’ that deepen the comprehension of the microscopic behaviour. Because of their predictive value, first-principles methods have also been used extensively to search for and to characterise new thermoelectric compounds. This chapter aims to illustrate the basic models used to guide the search for new thermoelectric materials and to provide ‘practical’ and introductory information to harvest the power of quantum mechanical calculations based on density functional theory (DFT).