During 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. INTRODUCTION Thermoelectric (TE) materials are materials that can generate useful electric potentials when subjected to a temperature gradient (known as the Seebeck effect). Conversely, they also transfer heat against the temperature gradient when a current is driven against this potential (known as the Peltier effect). They are promising energy materials with many applications, such as waste heat harvesting, radioisotope TE power generation, and solid state Peltier refrigeration, all of which are driving growing research interest. A key challenge is to improve the TE properties in order to obtain more efficient energy conversion and in turn enable new practical applications. Good TE materials must have excellent electrical transport properties, measured by the TE power factor ( = S 2 σ, where S is the Seebeck coefficient and σ is the electrical conductivity), and also a very low thermal conductivity κ (composed of the electronic contribution κ e , the lattice contribution κ L , and the bipolar contribution κ bi ). Combining the two aspects gives us the dimensionless figure of merit ZT,