Thermoelectric materials can convert waste heat into electric power and thus provide a way to reduce the dependence on fossil fuels. Our aim is to model the underlying materials properties and, in particular, the transport as controlled by electrons and lattice vibrations. The goal is to develop an understanding of the thermoelectric properties of selected materials at a fundamental level. The structural, electronic, optical, and phononic properties are studied in order to tune the transport, focusing on KxRhO2, NaxRhO2, PtSb2 and Bi2Se3. The investigations are based on density functional theory as implemented in the all electron linearized augmented plane wave plus local orbitals WIEN2k and pseudo potential Quantum-ESPRESSO codes. The thermoelectric properties are derived from Boltzmann transport theory under the constant relaxation time approximation, using the BoltzTraP code. We will discuss first the changes in the electronic band structure under variation of the cation concentration in layered KxRhO2 in the 2H phase and NaxRhO2 in the 3R phase. We will also study the hydrated phase. The deformations of the RhO6 octahedra turn out to govern the thermoelectric properties, where the high Seebeck coefficient results from ”pudding mold" bands. We investigate the thermoelectric properties of electron and hole doped PtSb2, which is not a layered material but shares “pudding mold" bands. PtSb2 has a high Seebeck coefficient at room temperature, which increases significantly under As alloying by bandgap opening and reduction of the lattice thermal conductivity. Bi2Se3 (bulk and thin film) has a larger bandgap then the well-known thermoelectric material Bi2Te3, which is important at high temperature. The structural stability, electronic structure, and transport properties of one to six quintuple layers of Bi2Se3 will be discussed. We also address the effect of strain on a single quintuple layer by phonon band structures. We will analyze the electronic and transport properties of Tl-doped Bi2Se3 under strain, focusing on the giant Rashba spin splitting (Tl doping breaks the inversion symmetry in Bi2Se3) and its dependence on biaxial tensile and compressive strain.