Within the context of the clay barrier concept for underground nuclear waste disposal, montmorillonite and bentonite have been widely used as reference materials for sorption. In some cases, accompanying modeling work aims at understanding and predicting sorption in complex natural systems where clays are assumed to be representative of the most reactive phases. This bottom-up approach relies heavily on good confidence in the mechanistic understanding of sorption phenomena. The present study aims at reviewing experimental and modeling work on montmorillonite with a focus on divalent metals experiencing pH dependent specific sorption. Current knowledge points out distinct sorption mechanisms on three types of sites: cation exchange on basal planes and surface complexation on edge surfaces with two types of sites: high energy (or strong) sites (HES) with high affinity for metals but low site density and low energy (or weak) sites (LES) with lower affinity for metals but high site density. Based on this current knowledge, criteria are given to select data relevant for surface complexation model calibration (especially ionic strength, pH, clay preparation and characterization, metal to clay ratio and solubility limits), with an emphasis on data uncertainties and reproducibility. Problematic experimental features are highlighted, especially those related to the reversibility of sorption and to the effect of the solid to liquid ratio (R-SL) on sorption distribution coefficients. Guidelines for data acquisition and selection are proposed. Surface complexation models available in the literature are then tested in terms of efficiency (data fit) and mechanistic likelihood. None of the currently available models is able to satisfy both aspects. Models directly adapted from oxide surface complexation models fail in both aspects. The most efficient model (in terms of simplicity and accuracy) is a non-electrostatic model. It is the only one that reproduces pH dependent specific sorption data at a low metal clay ratio (<0.001 mol/kg(clay); HES) in all selected experimental conditions, as well as data obtained at medium metal to clay ratio (similar to 0.01-0.05 mol/kg(clay); low energy sites). To account for physical mechanisms, an electrostatic surface complexation model has been developed. It takes into account the spill-over effect of negatively charged basal surfaces over edge surfaces, a typical feature of montmorillonite, and is able to reproduce sorption data for LES but not for HES. The reasons for this failure are explained through the mathematical derivations of model equations. This approach shows that it is impossible to reconcile HES properties with an oxide-like surface complexation electrostatic model. Amongst other alternatives, a successful electrostatic surface substitution model, which is compatible with current knowledge on HES structural properties, is proposed.