Researchers in thermoelectricity with backgrounds in non-equilibrium thermodynamics, thermoelectric engineering or condensed-matter physics tend to use di erent choices of ux densities and generalized forces. These choices are seldom justi ed from either the dissipation function or the entropy production rate. Because thermoelectric phenomena are a primary focus in several emerging elds, particularly in recent energy-oriented developments, a review of the di erent formalisms employed is judged timely. A systematic classi cation of the transport equations is presented here. The requirements on valid transport equations imposed by the invariance of the entropy production are clearly explained. The e ective Peltier and Seebeck coe cients, and the thermal conductivity, corresponding to the di erent choices of ux densities and generalized forces, are identi ed. Emphasis is made on illustrating the compatibility of apparently disparate formalisms. The advantages and drawbacks of these formalisms are discussed, especially from the point of view of the experimental determination of their thermoelectric coe cients.