Thermodynamic assessments of the pseudo-binary and -ternary systems formed by B2O3 with Na2O, Al2O3, and SiO2 were conducted according to the CALPHAD methodology. The compound energy formalism and two-sublattice partially ionic liquid models were used to thermodynamically represent the solid solutions malinkoite and mullite and the liquid phase of each system, respectively. A comprehensive literature review of available phase equilibria and thermodynamic experimental data as well as a detailed discussion of the modeling approaches implemented to optimize each system is provided. Assessment results are then presented and discussed, and the future path forward is outlined. The addition of B2O3 to the Na2O-Al2O3-SiO2 system contributes to the development of a thermodynamic database that will ultimately predict the equilibrium behavior of nepheline formation in high-level radioactive waste glass. (C) 2018 Elsevier Ltd.