AbstractDuring the last two decades, we have witnessed great progress in research on thermoelectrics. There are two primary focuses. One is the fundamental understanding of electrical and thermal transport, enabled by the interplay of theory and experiment; the other is the substantial enhancement of the performance of various thermoelectric materials, through synergistic optimisation of those intercorrelated transport parameters. Here we review some of the successful strategies for tuning electrical and thermal transport. For electrical transport, we start from the classical but still very active strategy of tuning band degeneracy (or band convergence), then discuss the engineering of carrier scattering, and finally address the concept of conduction channels and conductive networks that emerge in complex thermoelectric materials. For thermal transport, we summarise the approaches for studying thermal transport based on phonon–phonon interactions valid for conventional solids, as well as some quantitative efforts for nanostructures. We also discuss the thermal transport in complex materials with chemical-bond hierarchy, in which a portion of the atoms (or subunits) are weakly bonded to the rest of the structure, leading to an intrinsic manifestation of part-crystalline part-liquid state at elevated temperatures. In this review, we provide a summary of achievements made in recent studies of thermoelectric transport properties, and demonstrate how they have led to improvements in thermoelectric performance by the integration of modern theory and experiment, and point out some challenges and possible directions.