Thermoelectric power generation (TEG) represents one of the cleanest methods of energy conversion available today. It can be used in applications ranging from the harvesting of waste heat to conversion of solar energy into useful electricity. Remarkable advances have been achieved in recent years for various thermoelectric (TE) material systems. The introduction of nanostructures is used to tune the transport of phonons, while band structure engineering allows for the tailoring of electron transport. In this overview, top-down approaches to phonon engineering, such as atomic construction of new materials, will be reviewed. Bottom-up approaches to electron engineering, such as the formation of ordered nanostructures, will also be discussed. The assembly of TEG devices is still particularly challenging, and consequently, thermal-to-electric conversion utilizing these devices has been realized only in niche applications. In this review paper, we will discuss some of the challenges that must be overcome to enable widespread use of TE devices. These include thermal stability at the material level, and reliable contact at the device level.