The Seebeck coefficient is one of the key ingredients in thermoelectric properties, and it is often calculated based simply on the electronic band structure, within the frame of Boltzmann’s transport theory and the constant relaxation time approximation. Despite the simplicity and popularity of this approximation, its validity is not fully justified even in lightly doped semiconductors, and it breaks down completely in metals. On the other hand, more sophisticated first-principles approaches are available but require the computation of the full electron-phonon coupling. In this talk, I will discuss three cases comparing these two approaches: 1) Non-magnetic elemental metals viz., Li, Na, K, Cu, Ag, Au and Pt, some of which exhibit abnormal sign of the Seebeck coefficient [1]; 2) 3d ferromagnetic metals, viz. Fe, Co and Ni, whose transport properties are challenging to compute [2]; and 3) Electron-dope BaTiO3, in which a polar-to-nonpolar transition can occur upon doping and it may accompany abrupt changes in the resistivity and thermopower.