The author reworks his total current conductivity function introduced in a previous paper, related to electrical polarization of rocks in the frequency range of 1 MHz to 10−3 Hz. The original five parameters in this function are replaced by new ones, which from the beginning have clear petrophysical and electrochemical meanings and well-defined ranges of variation. Some classical models are derived as particular cases of it. The main existing models proposed to describe induced polarization (IP) are analyzed, and most of them are grouped together under a common circuit analog representation and a respective generating function. A circuit analog is assigned to each model. The multi-Cole–Cole model circuit analog reveals intrinsic constraints involving the values of its circuit elements. Because of these constraint relations and the relaxation times ratio (τ1/τ2)—usually many orders of magnitude from unity—the model has no physical validation to represent single-phase material systems (in the sense of the polarization). The performance and analysis of the various models to describe a few well-selected experimental data show that only two of the models, the multi-Cole–Cole and Dias models, can provide a function structure capable of fitting these data. This fact, the associated petrophysical interpretation consistency, and the basic characteristics of these two models, such as the way they were derived (empirically, the former; phenomenologically, the latter) and the number of coefficients in the function (directly related to the degree of ambiguity of their determination), make the author's model attractive and promising.