This paper describes the main thermodynamic concepts related to the construction of supplemented phase (or state) diagrams (SPDs) for aqueous solutions containing vitrifying agents used in the cryo- and dehydro-preservation of natural (foods, seeds, etc.) and synthetic (pharmaceuticals) products. It also reviews the empirical and theoretical equations employed to predict equilibrium transitions (ice freezing, solute solubility) and non-equilibrium transitions (glass transition and the extrapolated freezing curve). The comparison with experimental results is restricted to carbohydrate aqueous solutions, because these are the most widely used cryoprotectant agents. The paper identifies the best standard procedure to determine the glass transition curve over the entire water-content scale, and how to determine the temperature and concentration of the maximally freeze-concentrated solution.