This paper considers the state-of-the-art and open scientific and technological questions in thermoelectric materials and devices, from phonon engineering and scattering methods, to new and complex materials and their thermoelectric behavior. The paper also describes recent approaches to create structural and compositional material systems designed to enhance the thermoelectric figure of merit and power factors. We also summarize and contextualize recent advances in the use of superlattice structures and porosity or roughness to influence phonon scattering mechanisms and detail some advances in integrated thermoelectric materials for generators and coolers for thermally stable photonic devices. Controlling heat transport, dissipation and its conversion to other forms of energy are major research drivers for both materials researchers and device/product specialists alike.1,2 In parallel, nanoscale materials developments have provided insight and evidence for unusual and sometimes scalable phonon scattering phenomena to cause significant thermal conductivity suppression, often while maintaining electron conductivity in materials where electron specific heat contributions and other effects are controlled, such that relatively high thermoelectric figures of merit (ZT) can be obtained. The figure of merit Z T = S 2 σT /κ, where S = − V / T is the Seebeck coefficient ( V is the voltage difference caused by a temperature difference T ), σ is the electrical conductivity and κ is the thermal conductivity. Research and development in chip-or system-level cooling continuously provides the impetus for many of these developments, from semiconductor material cooling within a high clock-speed chip, to system level cooling of processors and data-farm thermal management.In tandem with thermal conductivity and transport control in materials and modules, is the necessity for understanding how material size, composition, structure and arrangement can alter phonon and heat transport, so that other research questions and technological advancements can be tackled. For instance, the required local (electrical) heating for phase change materials and memristors depends on thermal transport, heat dissipation and cooling to set the resistance memory or switching behavior. Annealing, sintering, and a host of other thermal treatments can influence and modify the physical properties of nanomaterial assemblies and thin films. The control and exploitation of these effects requires accurate measurement and interpretation of thermal transport to describe the important changes to composition, structure and arrangement caused at elevated temperature. There are many more cases where a more detailed understanding of heating and cooling for reasons other than power generation or thermoelectric control are important. In many cases, the experimental measurements are state-of-the-art and the modifications to the nature of the materials can often be very complex. 3 We summarize some of the * Electrochemical Society Member. z E-mail: c.odwyer@ucc.ie main a...