Based on the review of the phenomenological models of the Induced Polarization (IP), and the Electrical Double Layer theory, which is done in Part I, in Part 2, we review the capillary and granular models of porous media. These mechanistic models are derived for (i) an individual dielectric particle and (ii) a sequence of pores with different radii. For the polarizing spherical particle, following an approach of A. Revil, we show an easy way to upscale the particle response to the scale of the representative elementary volume. However, we stress that even the IP capillary model is “younger” than the IP granular model, the capillary model is less elaborated, and has not been properly upscaled. We believe this review will be useful for further development of specific IP theories for specific classes of soils, sediments, and rocks.