We study from first principles the transport properties of Al/AlOx/Al tunnel junctions. On this basis, we analyze the reliability of two analytical models for the conductance, namely the trapezoid potential barrier model and a tight-binding model. Our findings show that (i) the interface width used in the models is determined by the electronic density profile, and it is shorter than the width one expects from the atomic arrangements; (ii) the effective mass}, found to be about on third of the free electron mass, can be determined from the oxide band-structure calculations, and (iii) the barrier height is given by one fourth of the bandgap in the oxide, which explains the apparently small values found for these junctions experimentally.